YES
The TRS could be proven terminating. The proof took 4056 ms.
The following DP Processors were used
Problem 1 was processed with processor DependencyGraph (3907ms).
| – Problem 2 was processed with processor SubtermCriterion (3ms).
| – Problem 3 was processed with processor SubtermCriterion (2ms).
| – Problem 4 was processed with processor SubtermCriterion (2ms).
| – Problem 5 was processed with processor SubtermCriterion (2ms).
| – Problem 6 was processed with processor SubtermCriterion (2ms).
| | – Problem 13 was processed with processor DependencyGraph (9ms).
| – Problem 7 was processed with processor SubtermCriterion (44ms).
| – Problem 8 was processed with processor SubtermCriterion (2ms).
| – Problem 9 was processed with processor SubtermCriterion (2ms).
| – Problem 10 was processed with processor SubtermCriterion (2ms).
| – Problem 11 was processed with processor SubtermCriterion (2ms).
| – Problem 12 was processed with processor SubtermCriterion (2ms).
Problem 1: DependencyGraph
Dependency Pair Problem
Dependency Pairs
| eqt#(pid(N1), pid(N2)) | → | eqt#(N1, N2) | | eqs#(stack(E1, S1), stack(E2, S2)) | → | and#(eqt(E1, E2), eqs(S1, S2)) |
| eqc#(calls(E1, S1, CS1), calls(E2, S2, CS2)) | → | and#(eqt(E1, E2), and(eqs(S1, S2), eqc(CS1, CS2))) | | locker2_check_available#(Resource, cons(Lock, Locks)) | → | record_extract#(Lock, lock, resource) |
| eqt#(tuple(H1, T1), tuple(H2, T2)) | → | and#(eqt(H1, H2), eqt(T1, T2)) | | subtract#(List, cons(Head, Tail)) | → | delete#(Head, List) |
| locker2_map_promote_pending#(cons(Lock, Locks), Pending) | → | locker2_map_promote_pending#(Locks, Pending) | | eqs#(stack(E1, S1), stack(E2, S2)) | → | eqs#(S1, S2) |
| case6#(Locks, Lock, Resource, true) | → | record_extract#(Lock, lock, excl) | | locker2_obtainables#(cons(Lock, Locks), Client) | → | member#(Client, record_extract(Lock, lock, pending)) |
| locker2_obtainables#(cons(Lock, Locks), Client) | → | case5#(Client, Locks, Lock, member(Client, record_extract(Lock, lock, pending))) | | locker2_check_availables#(cons(Resource, Resources), Locks) | → | locker2_check_available#(Resource, Locks) |
| locker2_remove_pending#(Lock, Client) | → | record_extract#(Lock, lock, pending) | | istops#(E1, stack(E2, S1)) | → | eqt#(E1, E2) |
| locker2_check_availables#(cons(Resource, Resources), Locks) | → | locker2_check_availables#(Resources, Locks) | | locker2_obtainables#(cons(Lock, Locks), Client) | → | record_extract#(Lock, lock, pending) |
| case5#(Client, Locks, Lock, false) | → | locker2_obtainables#(Locks, Client) | | element#(int(s(s(N1))), tuple(T1, T2)) | → | element#(int(s(N1)), T2) |
| case9#(Tail, Head, E, false) | → | member#(E, Tail) | | locker2_add_pending#(Lock, Resources, Client) | → | member#(record_extract(Lock, lock, resource), Resources) |
| case6#(Locks, Lock, Resource, true) | → | record_extract#(Lock, lock, pending) | | locker2_promote_pending#(Lock, Client) | → | case0#(Client, Lock, record_extract(Lock, lock, pending)) |
| case8#(Tail, Head, E, false) | → | delete#(E, Tail) | | locker2_release_lock#(Lock, Client) | → | case2#(Client, Lock, gen_modtageq(Client, record_extract(Lock, lock, excl))) |
| case2#(Client, Lock, true) | → | record_updates#(Lock, lock, cons(tuple(excllock, excl), nil)) | | eqc#(calls(E1, S1, CS1), calls(E2, S2, CS2)) | → | eqc#(CS1, CS2) |
| eqt#(cons(H1, T1), cons(H2, T2)) | → | and#(eqt(H1, H2), eqt(T1, T2)) | | case0#(Client, Lock, cons(Client, Pendings)) | → | record_updates#(Lock, lock, cons(tuple(excl, tuplenil(Client)), cons(tuple(pending, tuplenil(Pendings)), nil))) |
| delete#(E, cons(Head, Tail)) | → | case8#(Tail, Head, E, equal(E, Head)) | | push#(E1, E2, calls(E3, S1, CS1)) | → | push1#(E1, E2, E3, S1, CS1, eqt(E1, E3)) |
| eqc#(calls(E1, S1, CS1), calls(E2, S2, CS2)) | → | eqs#(S1, S2) | | case1#(Client, Resources, Lock, true) | → | record_extract#(Lock, lock, pending) |
| append#(cons(Head, Tail), List) | → | append#(Tail, List) | | eqt#(tuplenil(H1), tuplenil(H2)) | → | eqt#(H1, H2) |
| locker2_check_available#(Resource, cons(Lock, Locks)) | → | case6#(Locks, Lock, Resource, equal(Resource, record_extract(Lock, lock, resource))) | | record_updates#(Record, Name, cons(tuple(Field, tuplenil(NewF)), Fields)) | → | record_updates#(record_update(Record, Name, Field, NewF), Name, Fields) |
| locker2_remove_pending#(Lock, Client) | → | subtract#(record_extract(Lock, lock, pending), cons(Client, nil)) | | case6#(Locks, Lock, Resource, false) | → | locker2_check_available#(Resource, Locks) |
| locker2_release_lock#(Lock, Client) | → | gen_modtageq#(Client, record_extract(Lock, lock, excl)) | | locker2_add_pending#(Lock, Resources, Client) | → | record_extract#(Lock, lock, resource) |
| eqt#(tuple(H1, T1), tuple(H2, T2)) | → | eqt#(T1, T2) | | locker2_remove_pending#(Lock, Client) | → | record_updates#(Lock, lock, cons(tuple(pending, tuplenil(subtract(record_extract(Lock, lock, pending), cons(Client, nil)))), nil)) |
| eqt#(cons(H1, T1), cons(H2, T2)) | → | eqt#(H1, H2) | | eqc#(calls(E1, S1, CS1), calls(E2, S2, CS2)) | → | eqt#(E1, E2) |
| eqs#(stack(E1, S1), stack(E2, S2)) | → | eqt#(E1, E2) | | locker2_map_claim_lock#(cons(Lock, Locks), Resources, Client) | → | locker2_map_claim_lock#(Locks, Resources, Client) |
| eqt#(tuple(H1, T1), tuple(H2, T2)) | → | eqt#(H1, H2) | | locker2_map_promote_pending#(cons(Lock, Locks), Pending) | → | locker2_promote_pending#(Lock, Pending) |
| case5#(Client, Locks, Lock, true) | → | locker2_obtainables#(Locks, Client) | | locker2_add_pending#(Lock, Resources, Client) | → | case1#(Client, Resources, Lock, member(record_extract(Lock, lock, resource), Resources)) |
| locker2_release_lock#(Lock, Client) | → | record_extract#(Lock, lock, excl) | | locker2_promote_pending#(Lock, Client) | → | record_extract#(Lock, lock, pending) |
| eqt#(cons(H1, T1), cons(H2, T2)) | → | eqt#(T1, T2) | | push1#(E1, E2, E3, S1, CS1, T) | → | pushs#(E2, S1) |
| record_updates#(Record, Name, cons(tuple(Field, tuplenil(NewF)), Fields)) | → | record_update#(Record, Name, Field, NewF) | | push#(E1, E2, calls(E3, S1, CS1)) | → | eqt#(E1, E3) |
| eqc#(calls(E1, S1, CS1), calls(E2, S2, CS2)) | → | and#(eqs(S1, S2), eqc(CS1, CS2)) | | subtract#(List, cons(Head, Tail)) | → | subtract#(delete(Head, List), Tail) |
| case1#(Client, Resources, Lock, true) | → | append#(record_extract(Lock, lock, pending), cons(Client, nil)) | | member#(E, cons(Head, Tail)) | → | case9#(Tail, Head, E, equal(E, Head)) |
| case1#(Client, Resources, Lock, true) | → | record_updates#(Lock, lock, cons(tuple(pending, tuplenil(append(record_extract(Lock, lock, pending), cons(Client, nil)))), nil)) |
Rewrite Rules
| or(T, T) | → | T | | or(F, T) | → | T |
| or(T, F) | → | T | | or(F, F) | → | F |
| and(T, B) | → | B | | and(B, T) | → | B |
| and(F, B) | → | F | | and(B, F) | → | F |
| imp(T, B) | → | B | | imp(F, B) | → | T |
| not(T) | → | F | | not(F) | → | T |
| if(T, B1, B2) | → | B1 | | if(F, B1, B2) | → | B2 |
| eq(T, T) | → | T | | eq(F, F) | → | T |
| eq(T, F) | → | F | | eq(F, T) | → | F |
| eqt(nil, undefined) | → | F | | eqt(nil, pid(N2)) | → | F |
| eqt(nil, int(N2)) | → | F | | eqt(nil, cons(H2, T2)) | → | F |
| eqt(nil, tuple(H2, T2)) | → | F | | eqt(nil, tuplenil(H2)) | → | F |
| eqt(a, nil) | → | F | | eqt(a, a) | → | T |
| eqt(a, excl) | → | F | | eqt(a, false) | → | F |
| eqt(a, lock) | → | F | | eqt(a, locker) | → | F |
| eqt(a, mcrlrecord) | → | F | | eqt(a, ok) | → | F |
| eqt(a, pending) | → | F | | eqt(a, release) | → | F |
| eqt(a, request) | → | F | | eqt(a, resource) | → | F |
| eqt(a, tag) | → | F | | eqt(a, true) | → | F |
| eqt(a, undefined) | → | F | | eqt(a, pid(N2)) | → | F |
| eqt(a, int(N2)) | → | F | | eqt(a, cons(H2, T2)) | → | F |
| eqt(a, tuple(H2, T2)) | → | F | | eqt(a, tuplenil(H2)) | → | F |
| eqt(excl, nil) | → | F | | eqt(excl, a) | → | F |
| eqt(excl, excl) | → | T | | eqt(excl, false) | → | F |
| eqt(excl, lock) | → | F | | eqt(excl, locker) | → | F |
| eqt(excl, mcrlrecord) | → | F | | eqt(excl, ok) | → | F |
| eqt(excl, pending) | → | F | | eqt(excl, release) | → | F |
| eqt(excl, request) | → | F | | eqt(excl, resource) | → | F |
| eqt(excl, tag) | → | F | | eqt(excl, true) | → | F |
| eqt(excl, undefined) | → | F | | eqt(excl, pid(N2)) | → | F |
| eqt(excl, eqt(false, int(N2))) | → | F | | eqt(false, cons(H2, T2)) | → | F |
| eqt(false, tuple(H2, T2)) | → | F | | eqt(false, tuplenil(H2)) | → | F |
| eqt(lock, nil) | → | F | | eqt(lock, a) | → | F |
| eqt(lock, excl) | → | F | | eqt(lock, false) | → | F |
| eqt(lock, lock) | → | T | | eqt(lock, locker) | → | F |
| eqt(lock, mcrlrecord) | → | F | | eqt(lock, ok) | → | F |
| eqt(lock, pending) | → | F | | eqt(lock, release) | → | F |
| eqt(lock, request) | → | F | | eqt(lock, resource) | → | F |
| eqt(lock, tag) | → | F | | eqt(lock, true) | → | F |
| eqt(lock, undefined) | → | F | | eqt(lock, pid(N2)) | → | F |
| eqt(lock, int(N2)) | → | F | | eqt(lock, cons(H2, T2)) | → | F |
| eqt(lock, tuple(H2, T2)) | → | F | | eqt(lock, tuplenil(H2)) | → | F |
| eqt(locker, nil) | → | F | | eqt(locker, a) | → | F |
| eqt(locker, excl) | → | F | | eqt(locker, false) | → | F |
| eqt(locker, lock) | → | F | | eqt(locker, locker) | → | T |
| eqt(locker, mcrlrecord) | → | F | | eqt(locker, ok) | → | F |
| eqt(locker, pending) | → | F | | eqt(locker, release) | → | F |
| eqt(locker, request) | → | F | | eqt(locker, resource) | → | F |
| eqt(locker, tag) | → | F | | eqt(locker, true) | → | F |
| eqt(locker, undefined) | → | F | | eqt(locker, pid(N2)) | → | F |
| eqt(locker, int(N2)) | → | F | | eqt(locker, cons(H2, T2)) | → | F |
| eqt(locker, tuple(H2, T2)) | → | F | | eqt(locker, tuplenil(H2)) | → | F |
| eqt(mcrlrecord, nil) | → | F | | eqt(mcrlrecord, a) | → | F |
| eqt(mcrlrecord, excl) | → | F | | eqt(mcrlrecord, false) | → | F |
| eqt(mcrlrecord, lock) | → | F | | eqt(mcrlrecord, locker) | → | F |
| eqt(mcrlrecord, mcrlrecord) | → | T | | eqt(mcrlrecord, ok) | → | F |
| eqt(mcrlrecord, pending) | → | F | | eqt(mcrlrecord, release) | → | F |
| eqt(mcrlrecord, request) | → | F | | eqt(mcrlrecord, resource) | → | F |
| eqt(ok, resource) | → | F | | eqt(ok, tag) | → | F |
| eqt(ok, true) | → | F | | eqt(ok, undefined) | → | F |
| eqt(ok, pid(N2)) | → | F | | eqt(ok, int(N2)) | → | F |
| eqt(ok, cons(H2, T2)) | → | F | | eqt(ok, tuple(H2, T2)) | → | F |
| eqt(ok, tuplenil(H2)) | → | F | | eqt(pending, nil) | → | F |
| eqt(pending, a) | → | F | | eqt(pending, excl) | → | F |
| eqt(pending, false) | → | F | | eqt(pending, lock) | → | F |
| eqt(pending, locker) | → | F | | eqt(pending, mcrlrecord) | → | F |
| eqt(pending, ok) | → | F | | eqt(pending, pending) | → | T |
| eqt(pending, release) | → | F | | eqt(pending, request) | → | F |
| eqt(pending, resource) | → | F | | eqt(pending, tag) | → | F |
| eqt(pending, true) | → | F | | eqt(pending, undefined) | → | F |
| eqt(pending, pid(N2)) | → | F | | eqt(pending, int(N2)) | → | F |
| eqt(pending, cons(H2, T2)) | → | F | | eqt(pending, tuple(H2, T2)) | → | F |
| eqt(pending, tuplenil(H2)) | → | F | | eqt(release, nil) | → | F |
| eqt(release, a) | → | F | | eqt(release, excl) | → | F |
| eqt(release, false) | → | F | | eqt(release, lock) | → | F |
| eqt(release, locker) | → | F | | eqt(release, mcrlrecord) | → | F |
| eqt(release, ok) | → | F | | eqt(request, mcrlrecord) | → | F |
| eqt(request, ok) | → | F | | eqt(request, pending) | → | F |
| eqt(request, release) | → | F | | eqt(request, request) | → | T |
| eqt(request, resource) | → | F | | eqt(request, tag) | → | F |
| eqt(request, true) | → | F | | eqt(request, undefined) | → | F |
| eqt(request, pid(N2)) | → | F | | eqt(request, int(N2)) | → | F |
| eqt(request, cons(H2, T2)) | → | F | | eqt(request, tuple(H2, T2)) | → | F |
| eqt(request, tuplenil(H2)) | → | F | | eqt(resource, nil) | → | F |
| eqt(resource, a) | → | F | | eqt(resource, excl) | → | F |
| eqt(resource, false) | → | F | | eqt(resource, lock) | → | F |
| eqt(resource, locker) | → | F | | eqt(resource, mcrlrecord) | → | F |
| eqt(resource, ok) | → | F | | eqt(resource, pending) | → | F |
| eqt(resource, release) | → | F | | eqt(resource, request) | → | F |
| eqt(resource, resource) | → | T | | eqt(resource, tag) | → | F |
| eqt(resource, true) | → | F | | eqt(resource, undefined) | → | F |
| eqt(resource, pid(N2)) | → | F | | eqt(resource, int(N2)) | → | F |
| eqt(resource, cons(H2, T2)) | → | F | | eqt(resource, tuple(H2, T2)) | → | F |
| eqt(resource, tuplenil(H2)) | → | F | | eqt(tag, nil) | → | F |
| eqt(tag, a) | → | F | | eqt(tag, excl) | → | F |
| eqt(tag, false) | → | F | | eqt(tag, lock) | → | F |
| eqt(tag, locker) | → | F | | eqt(tag, mcrlrecord) | → | F |
| eqt(tag, ok) | → | F | | eqt(tag, pending) | → | F |
| eqt(tag, release) | → | F | | eqt(tag, request) | → | F |
| eqt(tag, resource) | → | F | | eqt(tag, tag) | → | T |
| eqt(tag, true) | → | F | | eqt(tag, undefined) | → | F |
| eqt(tag, pid(N2)) | → | F | | eqt(tag, int(N2)) | → | F |
| eqt(tag, cons(H2, T2)) | → | F | | eqt(tag, tuple(H2, T2)) | → | F |
| eqt(tag, tuplenil(H2)) | → | F | | eqt(true, nil) | → | F |
| eqt(true, a) | → | F | | eqt(true, excl) | → | F |
| eqt(true, false) | → | F | | eqt(true, lock) | → | F |
| eqt(true, locker) | → | F | | eqt(true, mcrlrecord) | → | F |
| eqt(true, ok) | → | F | | eqt(true, pending) | → | F |
| eqt(true, release) | → | F | | eqt(true, request) | → | F |
| eqt(true, resource) | → | F | | eqt(true, tag) | → | F |
| eqt(true, true) | → | T | | eqt(true, undefined) | → | F |
| eqt(true, pid(N2)) | → | F | | eqt(true, int(N2)) | → | F |
| eqt(true, cons(H2, T2)) | → | F | | eqt(true, tuple(H2, T2)) | → | F |
| eqt(true, tuplenil(H2)) | → | F | | eqt(undefined, nil) | → | F |
| eqt(undefined, a) | → | F | | eqt(undefined, tuplenil(H2)) | → | F |
| eqt(pid(N1), nil) | → | F | | eqt(pid(N1), a) | → | F |
| eqt(pid(N1), excl) | → | F | | eqt(pid(N1), false) | → | F |
| eqt(pid(N1), lock) | → | F | | eqt(pid(N1), locker) | → | F |
| eqt(pid(N1), mcrlrecord) | → | F | | eqt(pid(N1), ok) | → | F |
| eqt(pid(N1), pending) | → | F | | eqt(pid(N1), release) | → | F |
| eqt(pid(N1), request) | → | F | | eqt(pid(N1), resource) | → | F |
| eqt(pid(N1), tag) | → | F | | eqt(pid(N1), true) | → | F |
| eqt(pid(N1), undefined) | → | F | | eqt(pid(N1), pid(N2)) | → | eqt(N1, N2) |
| eqt(pid(N1), int(N2)) | → | F | | eqt(pid(N1), cons(H2, T2)) | → | F |
| eqt(pid(N1), tuple(H2, T2)) | → | F | | eqt(pid(N1), tuplenil(H2)) | → | F |
| eqt(int(N1), nil) | → | F | | eqt(int(N1), a) | → | F |
| eqt(int(N1), excl) | → | F | | eqt(int(N1), false) | → | F |
| eqt(int(N1), lock) | → | F | | eqt(int(N1), locker) | → | F |
| eqt(int(N1), mcrlrecord) | → | F | | eqt(int(N1), ok) | → | F |
| eqt(int(N1), pending) | → | F | | eqt(int(N1), release) | → | F |
| eqt(int(N1), request) | → | F | | eqt(int(N1), resource) | → | F |
| eqt(int(N1), tag) | → | F | | eqt(int(N1), true) | → | F |
| eqt(int(N1), undefined) | → | F | | eqt(cons(H1, T1), resource) | → | F |
| eqt(cons(H1, T1), tag) | → | F | | eqt(cons(H1, T1), true) | → | F |
| eqt(cons(H1, T1), undefined) | → | F | | eqt(cons(H1, T1), pid(N2)) | → | F |
| eqt(cons(H1, T1), int(N2)) | → | F | | eqt(cons(H1, T1), cons(H2, T2)) | → | and(eqt(H1, H2), eqt(T1, T2)) |
| eqt(cons(H1, T1), tuple(H2, T2)) | → | F | | eqt(cons(H1, T1), tuplenil(H2)) | → | F |
| eqt(tuple(H1, T1), nil) | → | F | | eqt(tuple(H1, T1), a) | → | F |
| eqt(tuple(H1, T1), excl) | → | F | | eqt(tuple(H1, T1), false) | → | F |
| eqt(tuple(H1, T1), lock) | → | F | | eqt(tuple(H1, T1), locker) | → | F |
| eqt(tuple(H1, T1), mcrlrecord) | → | F | | eqt(tuple(H1, T1), ok) | → | F |
| eqt(tuple(H1, T1), pending) | → | F | | eqt(tuple(H1, T1), release) | → | F |
| eqt(tuple(H1, T1), request) | → | F | | eqt(tuple(H1, T1), resource) | → | F |
| eqt(tuple(H1, T1), tag) | → | F | | eqt(tuple(H1, T1), true) | → | F |
| eqt(tuple(H1, T1), undefined) | → | F | | eqt(tuple(H1, T1), pid(N2)) | → | F |
| eqt(tuple(H1, T1), int(N2)) | → | F | | eqt(tuple(H1, T1), cons(H2, T2)) | → | F |
| eqt(tuple(H1, T1), tuple(H2, T2)) | → | and(eqt(H1, H2), eqt(T1, T2)) | | eqt(tuple(H1, T1), tuplenil(H2)) | → | F |
| eqt(tuplenil(H1), nil) | → | F | | eqt(tuplenil(H1), a) | → | F |
| eqt(tuplenil(H1), excl) | → | F | | eqt(tuplenil(H1), false) | → | F |
| eqt(tuplenil(H1), lock) | → | F | | eqt(tuplenil(H1), locker) | → | F |
| eqt(tuplenil(H1), mcrlrecord) | → | F | | eqt(tuplenil(H1), ok) | → | F |
| eqt(tuplenil(H1), pending) | → | F | | eqt(tuplenil(H1), release) | → | F |
| eqt(tuplenil(H1), request) | → | F | | eqt(tuplenil(H1), resource) | → | F |
| eqt(tuplenil(H1), tag) | → | F | | eqt(tuplenil(H1), true) | → | F |
| eqt(tuplenil(H1), undefined) | → | F | | eqt(tuplenil(H1), pid(N2)) | → | F |
| eqt(tuplenil(H1), int(N2)) | → | F | | eqt(tuplenil(H1), cons(H2, T2)) | → | F |
| eqt(tuplenil(H1), tuple(H2, T2)) | → | F | | eqt(tuplenil(H1), tuplenil(H2)) | → | eqt(H1, H2) |
| element(int(s(0)), tuplenil(T1)) | → | T1 | | element(int(s(0)), tuple(T1, T2)) | → | T1 |
| element(int(s(s(N1))), tuple(T1, T2)) | → | element(int(s(N1)), T2) | | record_new(lock) | → | tuple(mcrlrecord, tuple(lock, tuple(undefined, tuple(nil, tuplenil(nil))))) |
| record_extract(tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2))))), lock, resource) | → | tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2))))) | | record_update(tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2))))), lock, pending, NewF) | → | tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(NewF))))) |
| record_updates(Record, Name, nil) | → | Record | | record_updates(Record, Name, cons(tuple(Field, tuplenil(NewF)), Fields)) | → | record_updates(record_update(Record, Name, Field, NewF), Name, Fields) |
| locker2_map_promote_pending(nil, Pending) | → | nil | | locker2_map_promote_pending(cons(Lock, Locks), Pending) | → | cons(locker2_promote_pending(Lock, Pending), locker2_map_promote_pending(Locks, Pending)) |
| locker2_map_claim_lock(nil, Resources, Client) | → | nil | | locker2_map_claim_lock(cons(Lock, Locks), Resources, Client) | → | cons(locker2_claim_lock(Lock, Resources, Client), locker2_map_claim_lock(Locks, Resources, Client)) |
| locker2_map_add_pending(nil, Resources, Client) | → | nil | | locker2_promote_pending(Lock, Client) | → | case0(Client, Lock, record_extract(Lock, lock, pending)) |
| case0(Client, Lock, cons(Client, Pendings)) | → | record_updates(Lock, lock, cons(tuple(excl, tuplenil(Client)), cons(tuple(pending, tuplenil(Pendings)), nil))) | | case0(Client, Lock, MCRLFree0) | → | Lock |
| locker2_remove_pending(Lock, Client) | → | record_updates(Lock, lock, cons(tuple(pending, tuplenil(subtract(record_extract(Lock, lock, pending), cons(Client, nil)))), nil)) | | locker2_add_pending(Lock, Resources, Client) | → | case1(Client, Resources, Lock, member(record_extract(Lock, lock, resource), Resources)) |
| case1(Client, Resources, Lock, true) | → | record_updates(Lock, lock, cons(tuple(pending, tuplenil(append(record_extract(Lock, lock, pending), cons(Client, nil)))), nil)) | | case1(Client, Resources, Lock, false) | → | Lock |
| locker2_release_lock(Lock, Client) | → | case2(Client, Lock, gen_modtageq(Client, record_extract(Lock, lock, excl))) | | case2(Client, Lock, true) | → | record_updates(Lock, lock, cons(tuple(excllock, excl), nil)) |
| case4(Client, Lock, MCRLFree1) | → | false | | locker2_obtainables(nil, Client) | → | true |
| locker2_obtainables(cons(Lock, Locks), Client) | → | case5(Client, Locks, Lock, member(Client, record_extract(Lock, lock, pending))) | | case5(Client, Locks, Lock, true) | → | andt(locker2_obtainable(Lock, Client), locker2_obtainables(Locks, Client)) |
| case5(Client, Locks, Lock, false) | → | locker2_obtainables(Locks, Client) | | locker2_check_available(Resource, nil) | → | false |
| locker2_check_available(Resource, cons(Lock, Locks)) | → | case6(Locks, Lock, Resource, equal(Resource, record_extract(Lock, lock, resource))) | | case6(Locks, Lock, Resource, true) | → | andt(equal(record_extract(Lock, lock, excl), nil), equal(record_extract(Lock, lock, pending), nil)) |
| case6(Locks, Lock, Resource, false) | → | locker2_check_available(Resource, Locks) | | locker2_check_availables(nil, Locks) | → | true |
| locker2_check_availables(cons(Resource, Resources), Locks) | → | andt(locker2_check_available(Resource, Locks), locker2_check_availables(Resources, Locks)) | | locker2_adduniq(nil, List) | → | List |
| append(cons(Head, Tail), List) | → | cons(Head, append(Tail, List)) | | subtract(List, nil) | → | List |
| subtract(List, cons(Head, Tail)) | → | subtract(delete(Head, List), Tail) | | delete(E, nil) | → | nil |
| delete(E, cons(Head, Tail)) | → | case8(Tail, Head, E, equal(E, Head)) | | case8(Tail, Head, E, true) | → | Tail |
| case8(Tail, Head, E, false) | → | cons(Head, delete(E, Tail)) | | gen_tag(Pid) | → | tuple(Pid, tuplenil(tag)) |
| gen_modtageq(Client1, Client2) | → | equal(Client1, Client2) | | member(E, nil) | → | false |
| member(E, cons(Head, Tail)) | → | case9(Tail, Head, E, equal(E, Head)) | | case9(Tail, Head, E, true) | → | true |
| case9(Tail, Head, E, false) | → | member(E, Tail) | | eqs(empty, empty) | → | T |
| eqs(empty, stack(E2, S2)) | → | F | | eqs(stack(E1, S1), empty) | → | F |
| eqs(stack(E1, S1), stack(E2, S2)) | → | and(eqt(E1, E2), eqs(S1, S2)) | | pushs(E1, S1) | → | stack(E1, S1) |
| pops(stack(E1, S1)) | → | S1 | | tops(stack(E1, S1)) | → | E1 |
| istops(E1, empty) | → | F | | istops(E1, stack(E2, S1)) | → | eqt(E1, E2) |
| eqc(nocalls, nocalls) | → | T | | eqc(nocalls, calls(E2, S2, CS2)) | → | F |
| eqc(calls(E1, S1, CS1), nocalls) | → | F | | eqc(calls(E1, S1, CS1), calls(E2, S2, CS2)) | → | and(eqt(E1, E2), and(eqs(S1, S2), eqc(CS1, CS2))) |
| push(E1, E2, nocalls) | → | calls(E1, stack(E2, empty), nocalls) | | push(E1, E2, calls(E3, S1, CS1)) | → | push1(E1, E2, E3, S1, CS1, eqt(E1, E3)) |
| push1(E1, E2, E3, S1, CS1, T) | → | calls(E3, pushs(E2, S1), CS1) |
Original Signature
Termination of terms over the following signature is verified: tuplenil, record_new, tuple, tag, gen_tag, imp, locker2_map_promote_pending, pops, locker2_check_availables, mcrlrecord, pending, request, empty, false, ok, istops, locker2_add_pending, andt, case2, append, element, case1, case0, tops, push1, case6, case5, or, int, case4, record_extract, locker, case9, case8, locker2_map_add_pending, calls, eqc, and, not, 0, locker2_promote_pending, locker2_claim_lock, locker2_adduniq, stack, release, locker2_obtainables, F, locker2_remove_pending, push, T, gen_modtageq, record_update, undefined, if, record_updates, eqt, excllock, delete, eqs, cons, member, locker2_map_claim_lock, locker2_obtainable, a, pushs, resource, lock, true, locker2_release_lock, pid, equal, subtract, locker2_check_available, s, excl, nil, eq, nocalls
Strategy
The following SCCs where found
| locker2_map_claim_lock#(cons(Lock, Locks), Resources, Client) → locker2_map_claim_lock#(Locks, Resources, Client) |
| eqt#(pid(N1), pid(N2)) → eqt#(N1, N2) | eqt#(tuple(H1, T1), tuple(H2, T2)) → eqt#(T1, T2) |
| eqt#(tuple(H1, T1), tuple(H2, T2)) → eqt#(H1, H2) | eqt#(cons(H1, T1), cons(H2, T2)) → eqt#(H1, H2) |
| eqt#(tuplenil(H1), tuplenil(H2)) → eqt#(H1, H2) | eqt#(cons(H1, T1), cons(H2, T2)) → eqt#(T1, T2) |
| append#(cons(Head, Tail), List) → append#(Tail, List) |
| eqc#(calls(E1, S1, CS1), calls(E2, S2, CS2)) → eqc#(CS1, CS2) |
| record_updates#(Record, Name, cons(tuple(Field, tuplenil(NewF)), Fields)) → record_updates#(record_update(Record, Name, Field, NewF), Name, Fields) |
| locker2_map_promote_pending#(cons(Lock, Locks), Pending) → locker2_map_promote_pending#(Locks, Pending) |
| subtract#(List, cons(Head, Tail)) → subtract#(delete(Head, List), Tail) |
| locker2_check_availables#(cons(Resource, Resources), Locks) → locker2_check_availables#(Resources, Locks) |
| eqs#(stack(E1, S1), stack(E2, S2)) → eqs#(S1, S2) |
| element#(int(s(s(N1))), tuple(T1, T2)) → element#(int(s(N1)), T2) |
| case5#(Client, Locks, Lock, true) → locker2_obtainables#(Locks, Client) | case5#(Client, Locks, Lock, false) → locker2_obtainables#(Locks, Client) |
| locker2_obtainables#(cons(Lock, Locks), Client) → case5#(Client, Locks, Lock, member(Client, record_extract(Lock, lock, pending))) |
Problem 2: SubtermCriterion
Dependency Pair Problem
Dependency Pairs
| locker2_map_promote_pending#(cons(Lock, Locks), Pending) | → | locker2_map_promote_pending#(Locks, Pending) |
Rewrite Rules
| or(T, T) | → | T | | or(F, T) | → | T |
| or(T, F) | → | T | | or(F, F) | → | F |
| and(T, B) | → | B | | and(B, T) | → | B |
| and(F, B) | → | F | | and(B, F) | → | F |
| imp(T, B) | → | B | | imp(F, B) | → | T |
| not(T) | → | F | | not(F) | → | T |
| if(T, B1, B2) | → | B1 | | if(F, B1, B2) | → | B2 |
| eq(T, T) | → | T | | eq(F, F) | → | T |
| eq(T, F) | → | F | | eq(F, T) | → | F |
| eqt(nil, undefined) | → | F | | eqt(nil, pid(N2)) | → | F |
| eqt(nil, int(N2)) | → | F | | eqt(nil, cons(H2, T2)) | → | F |
| eqt(nil, tuple(H2, T2)) | → | F | | eqt(nil, tuplenil(H2)) | → | F |
| eqt(a, nil) | → | F | | eqt(a, a) | → | T |
| eqt(a, excl) | → | F | | eqt(a, false) | → | F |
| eqt(a, lock) | → | F | | eqt(a, locker) | → | F |
| eqt(a, mcrlrecord) | → | F | | eqt(a, ok) | → | F |
| eqt(a, pending) | → | F | | eqt(a, release) | → | F |
| eqt(a, request) | → | F | | eqt(a, resource) | → | F |
| eqt(a, tag) | → | F | | eqt(a, true) | → | F |
| eqt(a, undefined) | → | F | | eqt(a, pid(N2)) | → | F |
| eqt(a, int(N2)) | → | F | | eqt(a, cons(H2, T2)) | → | F |
| eqt(a, tuple(H2, T2)) | → | F | | eqt(a, tuplenil(H2)) | → | F |
| eqt(excl, nil) | → | F | | eqt(excl, a) | → | F |
| eqt(excl, excl) | → | T | | eqt(excl, false) | → | F |
| eqt(excl, lock) | → | F | | eqt(excl, locker) | → | F |
| eqt(excl, mcrlrecord) | → | F | | eqt(excl, ok) | → | F |
| eqt(excl, pending) | → | F | | eqt(excl, release) | → | F |
| eqt(excl, request) | → | F | | eqt(excl, resource) | → | F |
| eqt(excl, tag) | → | F | | eqt(excl, true) | → | F |
| eqt(excl, undefined) | → | F | | eqt(excl, pid(N2)) | → | F |
| eqt(excl, eqt(false, int(N2))) | → | F | | eqt(false, cons(H2, T2)) | → | F |
| eqt(false, tuple(H2, T2)) | → | F | | eqt(false, tuplenil(H2)) | → | F |
| eqt(lock, nil) | → | F | | eqt(lock, a) | → | F |
| eqt(lock, excl) | → | F | | eqt(lock, false) | → | F |
| eqt(lock, lock) | → | T | | eqt(lock, locker) | → | F |
| eqt(lock, mcrlrecord) | → | F | | eqt(lock, ok) | → | F |
| eqt(lock, pending) | → | F | | eqt(lock, release) | → | F |
| eqt(lock, request) | → | F | | eqt(lock, resource) | → | F |
| eqt(lock, tag) | → | F | | eqt(lock, true) | → | F |
| eqt(lock, undefined) | → | F | | eqt(lock, pid(N2)) | → | F |
| eqt(lock, int(N2)) | → | F | | eqt(lock, cons(H2, T2)) | → | F |
| eqt(lock, tuple(H2, T2)) | → | F | | eqt(lock, tuplenil(H2)) | → | F |
| eqt(locker, nil) | → | F | | eqt(locker, a) | → | F |
| eqt(locker, excl) | → | F | | eqt(locker, false) | → | F |
| eqt(locker, lock) | → | F | | eqt(locker, locker) | → | T |
| eqt(locker, mcrlrecord) | → | F | | eqt(locker, ok) | → | F |
| eqt(locker, pending) | → | F | | eqt(locker, release) | → | F |
| eqt(locker, request) | → | F | | eqt(locker, resource) | → | F |
| eqt(locker, tag) | → | F | | eqt(locker, true) | → | F |
| eqt(locker, undefined) | → | F | | eqt(locker, pid(N2)) | → | F |
| eqt(locker, int(N2)) | → | F | | eqt(locker, cons(H2, T2)) | → | F |
| eqt(locker, tuple(H2, T2)) | → | F | | eqt(locker, tuplenil(H2)) | → | F |
| eqt(mcrlrecord, nil) | → | F | | eqt(mcrlrecord, a) | → | F |
| eqt(mcrlrecord, excl) | → | F | | eqt(mcrlrecord, false) | → | F |
| eqt(mcrlrecord, lock) | → | F | | eqt(mcrlrecord, locker) | → | F |
| eqt(mcrlrecord, mcrlrecord) | → | T | | eqt(mcrlrecord, ok) | → | F |
| eqt(mcrlrecord, pending) | → | F | | eqt(mcrlrecord, release) | → | F |
| eqt(mcrlrecord, request) | → | F | | eqt(mcrlrecord, resource) | → | F |
| eqt(ok, resource) | → | F | | eqt(ok, tag) | → | F |
| eqt(ok, true) | → | F | | eqt(ok, undefined) | → | F |
| eqt(ok, pid(N2)) | → | F | | eqt(ok, int(N2)) | → | F |
| eqt(ok, cons(H2, T2)) | → | F | | eqt(ok, tuple(H2, T2)) | → | F |
| eqt(ok, tuplenil(H2)) | → | F | | eqt(pending, nil) | → | F |
| eqt(pending, a) | → | F | | eqt(pending, excl) | → | F |
| eqt(pending, false) | → | F | | eqt(pending, lock) | → | F |
| eqt(pending, locker) | → | F | | eqt(pending, mcrlrecord) | → | F |
| eqt(pending, ok) | → | F | | eqt(pending, pending) | → | T |
| eqt(pending, release) | → | F | | eqt(pending, request) | → | F |
| eqt(pending, resource) | → | F | | eqt(pending, tag) | → | F |
| eqt(pending, true) | → | F | | eqt(pending, undefined) | → | F |
| eqt(pending, pid(N2)) | → | F | | eqt(pending, int(N2)) | → | F |
| eqt(pending, cons(H2, T2)) | → | F | | eqt(pending, tuple(H2, T2)) | → | F |
| eqt(pending, tuplenil(H2)) | → | F | | eqt(release, nil) | → | F |
| eqt(release, a) | → | F | | eqt(release, excl) | → | F |
| eqt(release, false) | → | F | | eqt(release, lock) | → | F |
| eqt(release, locker) | → | F | | eqt(release, mcrlrecord) | → | F |
| eqt(release, ok) | → | F | | eqt(request, mcrlrecord) | → | F |
| eqt(request, ok) | → | F | | eqt(request, pending) | → | F |
| eqt(request, release) | → | F | | eqt(request, request) | → | T |
| eqt(request, resource) | → | F | | eqt(request, tag) | → | F |
| eqt(request, true) | → | F | | eqt(request, undefined) | → | F |
| eqt(request, pid(N2)) | → | F | | eqt(request, int(N2)) | → | F |
| eqt(request, cons(H2, T2)) | → | F | | eqt(request, tuple(H2, T2)) | → | F |
| eqt(request, tuplenil(H2)) | → | F | | eqt(resource, nil) | → | F |
| eqt(resource, a) | → | F | | eqt(resource, excl) | → | F |
| eqt(resource, false) | → | F | | eqt(resource, lock) | → | F |
| eqt(resource, locker) | → | F | | eqt(resource, mcrlrecord) | → | F |
| eqt(resource, ok) | → | F | | eqt(resource, pending) | → | F |
| eqt(resource, release) | → | F | | eqt(resource, request) | → | F |
| eqt(resource, resource) | → | T | | eqt(resource, tag) | → | F |
| eqt(resource, true) | → | F | | eqt(resource, undefined) | → | F |
| eqt(resource, pid(N2)) | → | F | | eqt(resource, int(N2)) | → | F |
| eqt(resource, cons(H2, T2)) | → | F | | eqt(resource, tuple(H2, T2)) | → | F |
| eqt(resource, tuplenil(H2)) | → | F | | eqt(tag, nil) | → | F |
| eqt(tag, a) | → | F | | eqt(tag, excl) | → | F |
| eqt(tag, false) | → | F | | eqt(tag, lock) | → | F |
| eqt(tag, locker) | → | F | | eqt(tag, mcrlrecord) | → | F |
| eqt(tag, ok) | → | F | | eqt(tag, pending) | → | F |
| eqt(tag, release) | → | F | | eqt(tag, request) | → | F |
| eqt(tag, resource) | → | F | | eqt(tag, tag) | → | T |
| eqt(tag, true) | → | F | | eqt(tag, undefined) | → | F |
| eqt(tag, pid(N2)) | → | F | | eqt(tag, int(N2)) | → | F |
| eqt(tag, cons(H2, T2)) | → | F | | eqt(tag, tuple(H2, T2)) | → | F |
| eqt(tag, tuplenil(H2)) | → | F | | eqt(true, nil) | → | F |
| eqt(true, a) | → | F | | eqt(true, excl) | → | F |
| eqt(true, false) | → | F | | eqt(true, lock) | → | F |
| eqt(true, locker) | → | F | | eqt(true, mcrlrecord) | → | F |
| eqt(true, ok) | → | F | | eqt(true, pending) | → | F |
| eqt(true, release) | → | F | | eqt(true, request) | → | F |
| eqt(true, resource) | → | F | | eqt(true, tag) | → | F |
| eqt(true, true) | → | T | | eqt(true, undefined) | → | F |
| eqt(true, pid(N2)) | → | F | | eqt(true, int(N2)) | → | F |
| eqt(true, cons(H2, T2)) | → | F | | eqt(true, tuple(H2, T2)) | → | F |
| eqt(true, tuplenil(H2)) | → | F | | eqt(undefined, nil) | → | F |
| eqt(undefined, a) | → | F | | eqt(undefined, tuplenil(H2)) | → | F |
| eqt(pid(N1), nil) | → | F | | eqt(pid(N1), a) | → | F |
| eqt(pid(N1), excl) | → | F | | eqt(pid(N1), false) | → | F |
| eqt(pid(N1), lock) | → | F | | eqt(pid(N1), locker) | → | F |
| eqt(pid(N1), mcrlrecord) | → | F | | eqt(pid(N1), ok) | → | F |
| eqt(pid(N1), pending) | → | F | | eqt(pid(N1), release) | → | F |
| eqt(pid(N1), request) | → | F | | eqt(pid(N1), resource) | → | F |
| eqt(pid(N1), tag) | → | F | | eqt(pid(N1), true) | → | F |
| eqt(pid(N1), undefined) | → | F | | eqt(pid(N1), pid(N2)) | → | eqt(N1, N2) |
| eqt(pid(N1), int(N2)) | → | F | | eqt(pid(N1), cons(H2, T2)) | → | F |
| eqt(pid(N1), tuple(H2, T2)) | → | F | | eqt(pid(N1), tuplenil(H2)) | → | F |
| eqt(int(N1), nil) | → | F | | eqt(int(N1), a) | → | F |
| eqt(int(N1), excl) | → | F | | eqt(int(N1), false) | → | F |
| eqt(int(N1), lock) | → | F | | eqt(int(N1), locker) | → | F |
| eqt(int(N1), mcrlrecord) | → | F | | eqt(int(N1), ok) | → | F |
| eqt(int(N1), pending) | → | F | | eqt(int(N1), release) | → | F |
| eqt(int(N1), request) | → | F | | eqt(int(N1), resource) | → | F |
| eqt(int(N1), tag) | → | F | | eqt(int(N1), true) | → | F |
| eqt(int(N1), undefined) | → | F | | eqt(cons(H1, T1), resource) | → | F |
| eqt(cons(H1, T1), tag) | → | F | | eqt(cons(H1, T1), true) | → | F |
| eqt(cons(H1, T1), undefined) | → | F | | eqt(cons(H1, T1), pid(N2)) | → | F |
| eqt(cons(H1, T1), int(N2)) | → | F | | eqt(cons(H1, T1), cons(H2, T2)) | → | and(eqt(H1, H2), eqt(T1, T2)) |
| eqt(cons(H1, T1), tuple(H2, T2)) | → | F | | eqt(cons(H1, T1), tuplenil(H2)) | → | F |
| eqt(tuple(H1, T1), nil) | → | F | | eqt(tuple(H1, T1), a) | → | F |
| eqt(tuple(H1, T1), excl) | → | F | | eqt(tuple(H1, T1), false) | → | F |
| eqt(tuple(H1, T1), lock) | → | F | | eqt(tuple(H1, T1), locker) | → | F |
| eqt(tuple(H1, T1), mcrlrecord) | → | F | | eqt(tuple(H1, T1), ok) | → | F |
| eqt(tuple(H1, T1), pending) | → | F | | eqt(tuple(H1, T1), release) | → | F |
| eqt(tuple(H1, T1), request) | → | F | | eqt(tuple(H1, T1), resource) | → | F |
| eqt(tuple(H1, T1), tag) | → | F | | eqt(tuple(H1, T1), true) | → | F |
| eqt(tuple(H1, T1), undefined) | → | F | | eqt(tuple(H1, T1), pid(N2)) | → | F |
| eqt(tuple(H1, T1), int(N2)) | → | F | | eqt(tuple(H1, T1), cons(H2, T2)) | → | F |
| eqt(tuple(H1, T1), tuple(H2, T2)) | → | and(eqt(H1, H2), eqt(T1, T2)) | | eqt(tuple(H1, T1), tuplenil(H2)) | → | F |
| eqt(tuplenil(H1), nil) | → | F | | eqt(tuplenil(H1), a) | → | F |
| eqt(tuplenil(H1), excl) | → | F | | eqt(tuplenil(H1), false) | → | F |
| eqt(tuplenil(H1), lock) | → | F | | eqt(tuplenil(H1), locker) | → | F |
| eqt(tuplenil(H1), mcrlrecord) | → | F | | eqt(tuplenil(H1), ok) | → | F |
| eqt(tuplenil(H1), pending) | → | F | | eqt(tuplenil(H1), release) | → | F |
| eqt(tuplenil(H1), request) | → | F | | eqt(tuplenil(H1), resource) | → | F |
| eqt(tuplenil(H1), tag) | → | F | | eqt(tuplenil(H1), true) | → | F |
| eqt(tuplenil(H1), undefined) | → | F | | eqt(tuplenil(H1), pid(N2)) | → | F |
| eqt(tuplenil(H1), int(N2)) | → | F | | eqt(tuplenil(H1), cons(H2, T2)) | → | F |
| eqt(tuplenil(H1), tuple(H2, T2)) | → | F | | eqt(tuplenil(H1), tuplenil(H2)) | → | eqt(H1, H2) |
| element(int(s(0)), tuplenil(T1)) | → | T1 | | element(int(s(0)), tuple(T1, T2)) | → | T1 |
| element(int(s(s(N1))), tuple(T1, T2)) | → | element(int(s(N1)), T2) | | record_new(lock) | → | tuple(mcrlrecord, tuple(lock, tuple(undefined, tuple(nil, tuplenil(nil))))) |
| record_extract(tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2))))), lock, resource) | → | tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2))))) | | record_update(tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2))))), lock, pending, NewF) | → | tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(NewF))))) |
| record_updates(Record, Name, nil) | → | Record | | record_updates(Record, Name, cons(tuple(Field, tuplenil(NewF)), Fields)) | → | record_updates(record_update(Record, Name, Field, NewF), Name, Fields) |
| locker2_map_promote_pending(nil, Pending) | → | nil | | locker2_map_promote_pending(cons(Lock, Locks), Pending) | → | cons(locker2_promote_pending(Lock, Pending), locker2_map_promote_pending(Locks, Pending)) |
| locker2_map_claim_lock(nil, Resources, Client) | → | nil | | locker2_map_claim_lock(cons(Lock, Locks), Resources, Client) | → | cons(locker2_claim_lock(Lock, Resources, Client), locker2_map_claim_lock(Locks, Resources, Client)) |
| locker2_map_add_pending(nil, Resources, Client) | → | nil | | locker2_promote_pending(Lock, Client) | → | case0(Client, Lock, record_extract(Lock, lock, pending)) |
| case0(Client, Lock, cons(Client, Pendings)) | → | record_updates(Lock, lock, cons(tuple(excl, tuplenil(Client)), cons(tuple(pending, tuplenil(Pendings)), nil))) | | case0(Client, Lock, MCRLFree0) | → | Lock |
| locker2_remove_pending(Lock, Client) | → | record_updates(Lock, lock, cons(tuple(pending, tuplenil(subtract(record_extract(Lock, lock, pending), cons(Client, nil)))), nil)) | | locker2_add_pending(Lock, Resources, Client) | → | case1(Client, Resources, Lock, member(record_extract(Lock, lock, resource), Resources)) |
| case1(Client, Resources, Lock, true) | → | record_updates(Lock, lock, cons(tuple(pending, tuplenil(append(record_extract(Lock, lock, pending), cons(Client, nil)))), nil)) | | case1(Client, Resources, Lock, false) | → | Lock |
| locker2_release_lock(Lock, Client) | → | case2(Client, Lock, gen_modtageq(Client, record_extract(Lock, lock, excl))) | | case2(Client, Lock, true) | → | record_updates(Lock, lock, cons(tuple(excllock, excl), nil)) |
| case4(Client, Lock, MCRLFree1) | → | false | | locker2_obtainables(nil, Client) | → | true |
| locker2_obtainables(cons(Lock, Locks), Client) | → | case5(Client, Locks, Lock, member(Client, record_extract(Lock, lock, pending))) | | case5(Client, Locks, Lock, true) | → | andt(locker2_obtainable(Lock, Client), locker2_obtainables(Locks, Client)) |
| case5(Client, Locks, Lock, false) | → | locker2_obtainables(Locks, Client) | | locker2_check_available(Resource, nil) | → | false |
| locker2_check_available(Resource, cons(Lock, Locks)) | → | case6(Locks, Lock, Resource, equal(Resource, record_extract(Lock, lock, resource))) | | case6(Locks, Lock, Resource, true) | → | andt(equal(record_extract(Lock, lock, excl), nil), equal(record_extract(Lock, lock, pending), nil)) |
| case6(Locks, Lock, Resource, false) | → | locker2_check_available(Resource, Locks) | | locker2_check_availables(nil, Locks) | → | true |
| locker2_check_availables(cons(Resource, Resources), Locks) | → | andt(locker2_check_available(Resource, Locks), locker2_check_availables(Resources, Locks)) | | locker2_adduniq(nil, List) | → | List |
| append(cons(Head, Tail), List) | → | cons(Head, append(Tail, List)) | | subtract(List, nil) | → | List |
| subtract(List, cons(Head, Tail)) | → | subtract(delete(Head, List), Tail) | | delete(E, nil) | → | nil |
| delete(E, cons(Head, Tail)) | → | case8(Tail, Head, E, equal(E, Head)) | | case8(Tail, Head, E, true) | → | Tail |
| case8(Tail, Head, E, false) | → | cons(Head, delete(E, Tail)) | | gen_tag(Pid) | → | tuple(Pid, tuplenil(tag)) |
| gen_modtageq(Client1, Client2) | → | equal(Client1, Client2) | | member(E, nil) | → | false |
| member(E, cons(Head, Tail)) | → | case9(Tail, Head, E, equal(E, Head)) | | case9(Tail, Head, E, true) | → | true |
| case9(Tail, Head, E, false) | → | member(E, Tail) | | eqs(empty, empty) | → | T |
| eqs(empty, stack(E2, S2)) | → | F | | eqs(stack(E1, S1), empty) | → | F |
| eqs(stack(E1, S1), stack(E2, S2)) | → | and(eqt(E1, E2), eqs(S1, S2)) | | pushs(E1, S1) | → | stack(E1, S1) |
| pops(stack(E1, S1)) | → | S1 | | tops(stack(E1, S1)) | → | E1 |
| istops(E1, empty) | → | F | | istops(E1, stack(E2, S1)) | → | eqt(E1, E2) |
| eqc(nocalls, nocalls) | → | T | | eqc(nocalls, calls(E2, S2, CS2)) | → | F |
| eqc(calls(E1, S1, CS1), nocalls) | → | F | | eqc(calls(E1, S1, CS1), calls(E2, S2, CS2)) | → | and(eqt(E1, E2), and(eqs(S1, S2), eqc(CS1, CS2))) |
| push(E1, E2, nocalls) | → | calls(E1, stack(E2, empty), nocalls) | | push(E1, E2, calls(E3, S1, CS1)) | → | push1(E1, E2, E3, S1, CS1, eqt(E1, E3)) |
| push1(E1, E2, E3, S1, CS1, T) | → | calls(E3, pushs(E2, S1), CS1) |
Original Signature
Termination of terms over the following signature is verified: tuplenil, record_new, tuple, tag, gen_tag, imp, locker2_map_promote_pending, pops, locker2_check_availables, mcrlrecord, pending, request, empty, false, ok, istops, locker2_add_pending, andt, case2, append, element, case1, case0, tops, push1, case6, case5, or, int, case4, record_extract, locker, case9, case8, locker2_map_add_pending, calls, eqc, and, not, 0, locker2_promote_pending, locker2_claim_lock, locker2_adduniq, stack, release, locker2_obtainables, F, locker2_remove_pending, push, T, gen_modtageq, record_update, undefined, if, record_updates, eqt, excllock, delete, eqs, cons, member, locker2_map_claim_lock, locker2_obtainable, a, pushs, resource, lock, true, locker2_release_lock, pid, equal, subtract, locker2_check_available, s, excl, nil, eq, nocalls
Strategy
Projection
The following projection was used:
- π (locker2_map_promote_pending#): 1
Thus, the following dependency pairs are removed:
| locker2_map_promote_pending#(cons(Lock, Locks), Pending) | → | locker2_map_promote_pending#(Locks, Pending) |
Problem 3: SubtermCriterion
Dependency Pair Problem
Dependency Pairs
| element#(int(s(s(N1))), tuple(T1, T2)) | → | element#(int(s(N1)), T2) |
Rewrite Rules
| or(T, T) | → | T | | or(F, T) | → | T |
| or(T, F) | → | T | | or(F, F) | → | F |
| and(T, B) | → | B | | and(B, T) | → | B |
| and(F, B) | → | F | | and(B, F) | → | F |
| imp(T, B) | → | B | | imp(F, B) | → | T |
| not(T) | → | F | | not(F) | → | T |
| if(T, B1, B2) | → | B1 | | if(F, B1, B2) | → | B2 |
| eq(T, T) | → | T | | eq(F, F) | → | T |
| eq(T, F) | → | F | | eq(F, T) | → | F |
| eqt(nil, undefined) | → | F | | eqt(nil, pid(N2)) | → | F |
| eqt(nil, int(N2)) | → | F | | eqt(nil, cons(H2, T2)) | → | F |
| eqt(nil, tuple(H2, T2)) | → | F | | eqt(nil, tuplenil(H2)) | → | F |
| eqt(a, nil) | → | F | | eqt(a, a) | → | T |
| eqt(a, excl) | → | F | | eqt(a, false) | → | F |
| eqt(a, lock) | → | F | | eqt(a, locker) | → | F |
| eqt(a, mcrlrecord) | → | F | | eqt(a, ok) | → | F |
| eqt(a, pending) | → | F | | eqt(a, release) | → | F |
| eqt(a, request) | → | F | | eqt(a, resource) | → | F |
| eqt(a, tag) | → | F | | eqt(a, true) | → | F |
| eqt(a, undefined) | → | F | | eqt(a, pid(N2)) | → | F |
| eqt(a, int(N2)) | → | F | | eqt(a, cons(H2, T2)) | → | F |
| eqt(a, tuple(H2, T2)) | → | F | | eqt(a, tuplenil(H2)) | → | F |
| eqt(excl, nil) | → | F | | eqt(excl, a) | → | F |
| eqt(excl, excl) | → | T | | eqt(excl, false) | → | F |
| eqt(excl, lock) | → | F | | eqt(excl, locker) | → | F |
| eqt(excl, mcrlrecord) | → | F | | eqt(excl, ok) | → | F |
| eqt(excl, pending) | → | F | | eqt(excl, release) | → | F |
| eqt(excl, request) | → | F | | eqt(excl, resource) | → | F |
| eqt(excl, tag) | → | F | | eqt(excl, true) | → | F |
| eqt(excl, undefined) | → | F | | eqt(excl, pid(N2)) | → | F |
| eqt(excl, eqt(false, int(N2))) | → | F | | eqt(false, cons(H2, T2)) | → | F |
| eqt(false, tuple(H2, T2)) | → | F | | eqt(false, tuplenil(H2)) | → | F |
| eqt(lock, nil) | → | F | | eqt(lock, a) | → | F |
| eqt(lock, excl) | → | F | | eqt(lock, false) | → | F |
| eqt(lock, lock) | → | T | | eqt(lock, locker) | → | F |
| eqt(lock, mcrlrecord) | → | F | | eqt(lock, ok) | → | F |
| eqt(lock, pending) | → | F | | eqt(lock, release) | → | F |
| eqt(lock, request) | → | F | | eqt(lock, resource) | → | F |
| eqt(lock, tag) | → | F | | eqt(lock, true) | → | F |
| eqt(lock, undefined) | → | F | | eqt(lock, pid(N2)) | → | F |
| eqt(lock, int(N2)) | → | F | | eqt(lock, cons(H2, T2)) | → | F |
| eqt(lock, tuple(H2, T2)) | → | F | | eqt(lock, tuplenil(H2)) | → | F |
| eqt(locker, nil) | → | F | | eqt(locker, a) | → | F |
| eqt(locker, excl) | → | F | | eqt(locker, false) | → | F |
| eqt(locker, lock) | → | F | | eqt(locker, locker) | → | T |
| eqt(locker, mcrlrecord) | → | F | | eqt(locker, ok) | → | F |
| eqt(locker, pending) | → | F | | eqt(locker, release) | → | F |
| eqt(locker, request) | → | F | | eqt(locker, resource) | → | F |
| eqt(locker, tag) | → | F | | eqt(locker, true) | → | F |
| eqt(locker, undefined) | → | F | | eqt(locker, pid(N2)) | → | F |
| eqt(locker, int(N2)) | → | F | | eqt(locker, cons(H2, T2)) | → | F |
| eqt(locker, tuple(H2, T2)) | → | F | | eqt(locker, tuplenil(H2)) | → | F |
| eqt(mcrlrecord, nil) | → | F | | eqt(mcrlrecord, a) | → | F |
| eqt(mcrlrecord, excl) | → | F | | eqt(mcrlrecord, false) | → | F |
| eqt(mcrlrecord, lock) | → | F | | eqt(mcrlrecord, locker) | → | F |
| eqt(mcrlrecord, mcrlrecord) | → | T | | eqt(mcrlrecord, ok) | → | F |
| eqt(mcrlrecord, pending) | → | F | | eqt(mcrlrecord, release) | → | F |
| eqt(mcrlrecord, request) | → | F | | eqt(mcrlrecord, resource) | → | F |
| eqt(ok, resource) | → | F | | eqt(ok, tag) | → | F |
| eqt(ok, true) | → | F | | eqt(ok, undefined) | → | F |
| eqt(ok, pid(N2)) | → | F | | eqt(ok, int(N2)) | → | F |
| eqt(ok, cons(H2, T2)) | → | F | | eqt(ok, tuple(H2, T2)) | → | F |
| eqt(ok, tuplenil(H2)) | → | F | | eqt(pending, nil) | → | F |
| eqt(pending, a) | → | F | | eqt(pending, excl) | → | F |
| eqt(pending, false) | → | F | | eqt(pending, lock) | → | F |
| eqt(pending, locker) | → | F | | eqt(pending, mcrlrecord) | → | F |
| eqt(pending, ok) | → | F | | eqt(pending, pending) | → | T |
| eqt(pending, release) | → | F | | eqt(pending, request) | → | F |
| eqt(pending, resource) | → | F | | eqt(pending, tag) | → | F |
| eqt(pending, true) | → | F | | eqt(pending, undefined) | → | F |
| eqt(pending, pid(N2)) | → | F | | eqt(pending, int(N2)) | → | F |
| eqt(pending, cons(H2, T2)) | → | F | | eqt(pending, tuple(H2, T2)) | → | F |
| eqt(pending, tuplenil(H2)) | → | F | | eqt(release, nil) | → | F |
| eqt(release, a) | → | F | | eqt(release, excl) | → | F |
| eqt(release, false) | → | F | | eqt(release, lock) | → | F |
| eqt(release, locker) | → | F | | eqt(release, mcrlrecord) | → | F |
| eqt(release, ok) | → | F | | eqt(request, mcrlrecord) | → | F |
| eqt(request, ok) | → | F | | eqt(request, pending) | → | F |
| eqt(request, release) | → | F | | eqt(request, request) | → | T |
| eqt(request, resource) | → | F | | eqt(request, tag) | → | F |
| eqt(request, true) | → | F | | eqt(request, undefined) | → | F |
| eqt(request, pid(N2)) | → | F | | eqt(request, int(N2)) | → | F |
| eqt(request, cons(H2, T2)) | → | F | | eqt(request, tuple(H2, T2)) | → | F |
| eqt(request, tuplenil(H2)) | → | F | | eqt(resource, nil) | → | F |
| eqt(resource, a) | → | F | | eqt(resource, excl) | → | F |
| eqt(resource, false) | → | F | | eqt(resource, lock) | → | F |
| eqt(resource, locker) | → | F | | eqt(resource, mcrlrecord) | → | F |
| eqt(resource, ok) | → | F | | eqt(resource, pending) | → | F |
| eqt(resource, release) | → | F | | eqt(resource, request) | → | F |
| eqt(resource, resource) | → | T | | eqt(resource, tag) | → | F |
| eqt(resource, true) | → | F | | eqt(resource, undefined) | → | F |
| eqt(resource, pid(N2)) | → | F | | eqt(resource, int(N2)) | → | F |
| eqt(resource, cons(H2, T2)) | → | F | | eqt(resource, tuple(H2, T2)) | → | F |
| eqt(resource, tuplenil(H2)) | → | F | | eqt(tag, nil) | → | F |
| eqt(tag, a) | → | F | | eqt(tag, excl) | → | F |
| eqt(tag, false) | → | F | | eqt(tag, lock) | → | F |
| eqt(tag, locker) | → | F | | eqt(tag, mcrlrecord) | → | F |
| eqt(tag, ok) | → | F | | eqt(tag, pending) | → | F |
| eqt(tag, release) | → | F | | eqt(tag, request) | → | F |
| eqt(tag, resource) | → | F | | eqt(tag, tag) | → | T |
| eqt(tag, true) | → | F | | eqt(tag, undefined) | → | F |
| eqt(tag, pid(N2)) | → | F | | eqt(tag, int(N2)) | → | F |
| eqt(tag, cons(H2, T2)) | → | F | | eqt(tag, tuple(H2, T2)) | → | F |
| eqt(tag, tuplenil(H2)) | → | F | | eqt(true, nil) | → | F |
| eqt(true, a) | → | F | | eqt(true, excl) | → | F |
| eqt(true, false) | → | F | | eqt(true, lock) | → | F |
| eqt(true, locker) | → | F | | eqt(true, mcrlrecord) | → | F |
| eqt(true, ok) | → | F | | eqt(true, pending) | → | F |
| eqt(true, release) | → | F | | eqt(true, request) | → | F |
| eqt(true, resource) | → | F | | eqt(true, tag) | → | F |
| eqt(true, true) | → | T | | eqt(true, undefined) | → | F |
| eqt(true, pid(N2)) | → | F | | eqt(true, int(N2)) | → | F |
| eqt(true, cons(H2, T2)) | → | F | | eqt(true, tuple(H2, T2)) | → | F |
| eqt(true, tuplenil(H2)) | → | F | | eqt(undefined, nil) | → | F |
| eqt(undefined, a) | → | F | | eqt(undefined, tuplenil(H2)) | → | F |
| eqt(pid(N1), nil) | → | F | | eqt(pid(N1), a) | → | F |
| eqt(pid(N1), excl) | → | F | | eqt(pid(N1), false) | → | F |
| eqt(pid(N1), lock) | → | F | | eqt(pid(N1), locker) | → | F |
| eqt(pid(N1), mcrlrecord) | → | F | | eqt(pid(N1), ok) | → | F |
| eqt(pid(N1), pending) | → | F | | eqt(pid(N1), release) | → | F |
| eqt(pid(N1), request) | → | F | | eqt(pid(N1), resource) | → | F |
| eqt(pid(N1), tag) | → | F | | eqt(pid(N1), true) | → | F |
| eqt(pid(N1), undefined) | → | F | | eqt(pid(N1), pid(N2)) | → | eqt(N1, N2) |
| eqt(pid(N1), int(N2)) | → | F | | eqt(pid(N1), cons(H2, T2)) | → | F |
| eqt(pid(N1), tuple(H2, T2)) | → | F | | eqt(pid(N1), tuplenil(H2)) | → | F |
| eqt(int(N1), nil) | → | F | | eqt(int(N1), a) | → | F |
| eqt(int(N1), excl) | → | F | | eqt(int(N1), false) | → | F |
| eqt(int(N1), lock) | → | F | | eqt(int(N1), locker) | → | F |
| eqt(int(N1), mcrlrecord) | → | F | | eqt(int(N1), ok) | → | F |
| eqt(int(N1), pending) | → | F | | eqt(int(N1), release) | → | F |
| eqt(int(N1), request) | → | F | | eqt(int(N1), resource) | → | F |
| eqt(int(N1), tag) | → | F | | eqt(int(N1), true) | → | F |
| eqt(int(N1), undefined) | → | F | | eqt(cons(H1, T1), resource) | → | F |
| eqt(cons(H1, T1), tag) | → | F | | eqt(cons(H1, T1), true) | → | F |
| eqt(cons(H1, T1), undefined) | → | F | | eqt(cons(H1, T1), pid(N2)) | → | F |
| eqt(cons(H1, T1), int(N2)) | → | F | | eqt(cons(H1, T1), cons(H2, T2)) | → | and(eqt(H1, H2), eqt(T1, T2)) |
| eqt(cons(H1, T1), tuple(H2, T2)) | → | F | | eqt(cons(H1, T1), tuplenil(H2)) | → | F |
| eqt(tuple(H1, T1), nil) | → | F | | eqt(tuple(H1, T1), a) | → | F |
| eqt(tuple(H1, T1), excl) | → | F | | eqt(tuple(H1, T1), false) | → | F |
| eqt(tuple(H1, T1), lock) | → | F | | eqt(tuple(H1, T1), locker) | → | F |
| eqt(tuple(H1, T1), mcrlrecord) | → | F | | eqt(tuple(H1, T1), ok) | → | F |
| eqt(tuple(H1, T1), pending) | → | F | | eqt(tuple(H1, T1), release) | → | F |
| eqt(tuple(H1, T1), request) | → | F | | eqt(tuple(H1, T1), resource) | → | F |
| eqt(tuple(H1, T1), tag) | → | F | | eqt(tuple(H1, T1), true) | → | F |
| eqt(tuple(H1, T1), undefined) | → | F | | eqt(tuple(H1, T1), pid(N2)) | → | F |
| eqt(tuple(H1, T1), int(N2)) | → | F | | eqt(tuple(H1, T1), cons(H2, T2)) | → | F |
| eqt(tuple(H1, T1), tuple(H2, T2)) | → | and(eqt(H1, H2), eqt(T1, T2)) | | eqt(tuple(H1, T1), tuplenil(H2)) | → | F |
| eqt(tuplenil(H1), nil) | → | F | | eqt(tuplenil(H1), a) | → | F |
| eqt(tuplenil(H1), excl) | → | F | | eqt(tuplenil(H1), false) | → | F |
| eqt(tuplenil(H1), lock) | → | F | | eqt(tuplenil(H1), locker) | → | F |
| eqt(tuplenil(H1), mcrlrecord) | → | F | | eqt(tuplenil(H1), ok) | → | F |
| eqt(tuplenil(H1), pending) | → | F | | eqt(tuplenil(H1), release) | → | F |
| eqt(tuplenil(H1), request) | → | F | | eqt(tuplenil(H1), resource) | → | F |
| eqt(tuplenil(H1), tag) | → | F | | eqt(tuplenil(H1), true) | → | F |
| eqt(tuplenil(H1), undefined) | → | F | | eqt(tuplenil(H1), pid(N2)) | → | F |
| eqt(tuplenil(H1), int(N2)) | → | F | | eqt(tuplenil(H1), cons(H2, T2)) | → | F |
| eqt(tuplenil(H1), tuple(H2, T2)) | → | F | | eqt(tuplenil(H1), tuplenil(H2)) | → | eqt(H1, H2) |
| element(int(s(0)), tuplenil(T1)) | → | T1 | | element(int(s(0)), tuple(T1, T2)) | → | T1 |
| element(int(s(s(N1))), tuple(T1, T2)) | → | element(int(s(N1)), T2) | | record_new(lock) | → | tuple(mcrlrecord, tuple(lock, tuple(undefined, tuple(nil, tuplenil(nil))))) |
| record_extract(tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2))))), lock, resource) | → | tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2))))) | | record_update(tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2))))), lock, pending, NewF) | → | tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(NewF))))) |
| record_updates(Record, Name, nil) | → | Record | | record_updates(Record, Name, cons(tuple(Field, tuplenil(NewF)), Fields)) | → | record_updates(record_update(Record, Name, Field, NewF), Name, Fields) |
| locker2_map_promote_pending(nil, Pending) | → | nil | | locker2_map_promote_pending(cons(Lock, Locks), Pending) | → | cons(locker2_promote_pending(Lock, Pending), locker2_map_promote_pending(Locks, Pending)) |
| locker2_map_claim_lock(nil, Resources, Client) | → | nil | | locker2_map_claim_lock(cons(Lock, Locks), Resources, Client) | → | cons(locker2_claim_lock(Lock, Resources, Client), locker2_map_claim_lock(Locks, Resources, Client)) |
| locker2_map_add_pending(nil, Resources, Client) | → | nil | | locker2_promote_pending(Lock, Client) | → | case0(Client, Lock, record_extract(Lock, lock, pending)) |
| case0(Client, Lock, cons(Client, Pendings)) | → | record_updates(Lock, lock, cons(tuple(excl, tuplenil(Client)), cons(tuple(pending, tuplenil(Pendings)), nil))) | | case0(Client, Lock, MCRLFree0) | → | Lock |
| locker2_remove_pending(Lock, Client) | → | record_updates(Lock, lock, cons(tuple(pending, tuplenil(subtract(record_extract(Lock, lock, pending), cons(Client, nil)))), nil)) | | locker2_add_pending(Lock, Resources, Client) | → | case1(Client, Resources, Lock, member(record_extract(Lock, lock, resource), Resources)) |
| case1(Client, Resources, Lock, true) | → | record_updates(Lock, lock, cons(tuple(pending, tuplenil(append(record_extract(Lock, lock, pending), cons(Client, nil)))), nil)) | | case1(Client, Resources, Lock, false) | → | Lock |
| locker2_release_lock(Lock, Client) | → | case2(Client, Lock, gen_modtageq(Client, record_extract(Lock, lock, excl))) | | case2(Client, Lock, true) | → | record_updates(Lock, lock, cons(tuple(excllock, excl), nil)) |
| case4(Client, Lock, MCRLFree1) | → | false | | locker2_obtainables(nil, Client) | → | true |
| locker2_obtainables(cons(Lock, Locks), Client) | → | case5(Client, Locks, Lock, member(Client, record_extract(Lock, lock, pending))) | | case5(Client, Locks, Lock, true) | → | andt(locker2_obtainable(Lock, Client), locker2_obtainables(Locks, Client)) |
| case5(Client, Locks, Lock, false) | → | locker2_obtainables(Locks, Client) | | locker2_check_available(Resource, nil) | → | false |
| locker2_check_available(Resource, cons(Lock, Locks)) | → | case6(Locks, Lock, Resource, equal(Resource, record_extract(Lock, lock, resource))) | | case6(Locks, Lock, Resource, true) | → | andt(equal(record_extract(Lock, lock, excl), nil), equal(record_extract(Lock, lock, pending), nil)) |
| case6(Locks, Lock, Resource, false) | → | locker2_check_available(Resource, Locks) | | locker2_check_availables(nil, Locks) | → | true |
| locker2_check_availables(cons(Resource, Resources), Locks) | → | andt(locker2_check_available(Resource, Locks), locker2_check_availables(Resources, Locks)) | | locker2_adduniq(nil, List) | → | List |
| append(cons(Head, Tail), List) | → | cons(Head, append(Tail, List)) | | subtract(List, nil) | → | List |
| subtract(List, cons(Head, Tail)) | → | subtract(delete(Head, List), Tail) | | delete(E, nil) | → | nil |
| delete(E, cons(Head, Tail)) | → | case8(Tail, Head, E, equal(E, Head)) | | case8(Tail, Head, E, true) | → | Tail |
| case8(Tail, Head, E, false) | → | cons(Head, delete(E, Tail)) | | gen_tag(Pid) | → | tuple(Pid, tuplenil(tag)) |
| gen_modtageq(Client1, Client2) | → | equal(Client1, Client2) | | member(E, nil) | → | false |
| member(E, cons(Head, Tail)) | → | case9(Tail, Head, E, equal(E, Head)) | | case9(Tail, Head, E, true) | → | true |
| case9(Tail, Head, E, false) | → | member(E, Tail) | | eqs(empty, empty) | → | T |
| eqs(empty, stack(E2, S2)) | → | F | | eqs(stack(E1, S1), empty) | → | F |
| eqs(stack(E1, S1), stack(E2, S2)) | → | and(eqt(E1, E2), eqs(S1, S2)) | | pushs(E1, S1) | → | stack(E1, S1) |
| pops(stack(E1, S1)) | → | S1 | | tops(stack(E1, S1)) | → | E1 |
| istops(E1, empty) | → | F | | istops(E1, stack(E2, S1)) | → | eqt(E1, E2) |
| eqc(nocalls, nocalls) | → | T | | eqc(nocalls, calls(E2, S2, CS2)) | → | F |
| eqc(calls(E1, S1, CS1), nocalls) | → | F | | eqc(calls(E1, S1, CS1), calls(E2, S2, CS2)) | → | and(eqt(E1, E2), and(eqs(S1, S2), eqc(CS1, CS2))) |
| push(E1, E2, nocalls) | → | calls(E1, stack(E2, empty), nocalls) | | push(E1, E2, calls(E3, S1, CS1)) | → | push1(E1, E2, E3, S1, CS1, eqt(E1, E3)) |
| push1(E1, E2, E3, S1, CS1, T) | → | calls(E3, pushs(E2, S1), CS1) |
Original Signature
Termination of terms over the following signature is verified: tuplenil, record_new, tuple, tag, gen_tag, imp, locker2_map_promote_pending, pops, locker2_check_availables, mcrlrecord, pending, request, empty, false, ok, istops, locker2_add_pending, andt, case2, append, element, case1, case0, tops, push1, case6, case5, or, int, case4, record_extract, locker, case9, case8, locker2_map_add_pending, calls, eqc, and, not, 0, locker2_promote_pending, locker2_claim_lock, locker2_adduniq, stack, release, locker2_obtainables, F, locker2_remove_pending, push, T, gen_modtageq, record_update, undefined, if, record_updates, eqt, excllock, delete, eqs, cons, member, locker2_map_claim_lock, locker2_obtainable, a, pushs, resource, lock, true, locker2_release_lock, pid, equal, subtract, locker2_check_available, s, excl, nil, eq, nocalls
Strategy
Projection
The following projection was used:
Thus, the following dependency pairs are removed:
| element#(int(s(s(N1))), tuple(T1, T2)) | → | element#(int(s(N1)), T2) |
Problem 4: SubtermCriterion
Dependency Pair Problem
Dependency Pairs
| subtract#(List, cons(Head, Tail)) | → | subtract#(delete(Head, List), Tail) |
Rewrite Rules
| or(T, T) | → | T | | or(F, T) | → | T |
| or(T, F) | → | T | | or(F, F) | → | F |
| and(T, B) | → | B | | and(B, T) | → | B |
| and(F, B) | → | F | | and(B, F) | → | F |
| imp(T, B) | → | B | | imp(F, B) | → | T |
| not(T) | → | F | | not(F) | → | T |
| if(T, B1, B2) | → | B1 | | if(F, B1, B2) | → | B2 |
| eq(T, T) | → | T | | eq(F, F) | → | T |
| eq(T, F) | → | F | | eq(F, T) | → | F |
| eqt(nil, undefined) | → | F | | eqt(nil, pid(N2)) | → | F |
| eqt(nil, int(N2)) | → | F | | eqt(nil, cons(H2, T2)) | → | F |
| eqt(nil, tuple(H2, T2)) | → | F | | eqt(nil, tuplenil(H2)) | → | F |
| eqt(a, nil) | → | F | | eqt(a, a) | → | T |
| eqt(a, excl) | → | F | | eqt(a, false) | → | F |
| eqt(a, lock) | → | F | | eqt(a, locker) | → | F |
| eqt(a, mcrlrecord) | → | F | | eqt(a, ok) | → | F |
| eqt(a, pending) | → | F | | eqt(a, release) | → | F |
| eqt(a, request) | → | F | | eqt(a, resource) | → | F |
| eqt(a, tag) | → | F | | eqt(a, true) | → | F |
| eqt(a, undefined) | → | F | | eqt(a, pid(N2)) | → | F |
| eqt(a, int(N2)) | → | F | | eqt(a, cons(H2, T2)) | → | F |
| eqt(a, tuple(H2, T2)) | → | F | | eqt(a, tuplenil(H2)) | → | F |
| eqt(excl, nil) | → | F | | eqt(excl, a) | → | F |
| eqt(excl, excl) | → | T | | eqt(excl, false) | → | F |
| eqt(excl, lock) | → | F | | eqt(excl, locker) | → | F |
| eqt(excl, mcrlrecord) | → | F | | eqt(excl, ok) | → | F |
| eqt(excl, pending) | → | F | | eqt(excl, release) | → | F |
| eqt(excl, request) | → | F | | eqt(excl, resource) | → | F |
| eqt(excl, tag) | → | F | | eqt(excl, true) | → | F |
| eqt(excl, undefined) | → | F | | eqt(excl, pid(N2)) | → | F |
| eqt(excl, eqt(false, int(N2))) | → | F | | eqt(false, cons(H2, T2)) | → | F |
| eqt(false, tuple(H2, T2)) | → | F | | eqt(false, tuplenil(H2)) | → | F |
| eqt(lock, nil) | → | F | | eqt(lock, a) | → | F |
| eqt(lock, excl) | → | F | | eqt(lock, false) | → | F |
| eqt(lock, lock) | → | T | | eqt(lock, locker) | → | F |
| eqt(lock, mcrlrecord) | → | F | | eqt(lock, ok) | → | F |
| eqt(lock, pending) | → | F | | eqt(lock, release) | → | F |
| eqt(lock, request) | → | F | | eqt(lock, resource) | → | F |
| eqt(lock, tag) | → | F | | eqt(lock, true) | → | F |
| eqt(lock, undefined) | → | F | | eqt(lock, pid(N2)) | → | F |
| eqt(lock, int(N2)) | → | F | | eqt(lock, cons(H2, T2)) | → | F |
| eqt(lock, tuple(H2, T2)) | → | F | | eqt(lock, tuplenil(H2)) | → | F |
| eqt(locker, nil) | → | F | | eqt(locker, a) | → | F |
| eqt(locker, excl) | → | F | | eqt(locker, false) | → | F |
| eqt(locker, lock) | → | F | | eqt(locker, locker) | → | T |
| eqt(locker, mcrlrecord) | → | F | | eqt(locker, ok) | → | F |
| eqt(locker, pending) | → | F | | eqt(locker, release) | → | F |
| eqt(locker, request) | → | F | | eqt(locker, resource) | → | F |
| eqt(locker, tag) | → | F | | eqt(locker, true) | → | F |
| eqt(locker, undefined) | → | F | | eqt(locker, pid(N2)) | → | F |
| eqt(locker, int(N2)) | → | F | | eqt(locker, cons(H2, T2)) | → | F |
| eqt(locker, tuple(H2, T2)) | → | F | | eqt(locker, tuplenil(H2)) | → | F |
| eqt(mcrlrecord, nil) | → | F | | eqt(mcrlrecord, a) | → | F |
| eqt(mcrlrecord, excl) | → | F | | eqt(mcrlrecord, false) | → | F |
| eqt(mcrlrecord, lock) | → | F | | eqt(mcrlrecord, locker) | → | F |
| eqt(mcrlrecord, mcrlrecord) | → | T | | eqt(mcrlrecord, ok) | → | F |
| eqt(mcrlrecord, pending) | → | F | | eqt(mcrlrecord, release) | → | F |
| eqt(mcrlrecord, request) | → | F | | eqt(mcrlrecord, resource) | → | F |
| eqt(ok, resource) | → | F | | eqt(ok, tag) | → | F |
| eqt(ok, true) | → | F | | eqt(ok, undefined) | → | F |
| eqt(ok, pid(N2)) | → | F | | eqt(ok, int(N2)) | → | F |
| eqt(ok, cons(H2, T2)) | → | F | | eqt(ok, tuple(H2, T2)) | → | F |
| eqt(ok, tuplenil(H2)) | → | F | | eqt(pending, nil) | → | F |
| eqt(pending, a) | → | F | | eqt(pending, excl) | → | F |
| eqt(pending, false) | → | F | | eqt(pending, lock) | → | F |
| eqt(pending, locker) | → | F | | eqt(pending, mcrlrecord) | → | F |
| eqt(pending, ok) | → | F | | eqt(pending, pending) | → | T |
| eqt(pending, release) | → | F | | eqt(pending, request) | → | F |
| eqt(pending, resource) | → | F | | eqt(pending, tag) | → | F |
| eqt(pending, true) | → | F | | eqt(pending, undefined) | → | F |
| eqt(pending, pid(N2)) | → | F | | eqt(pending, int(N2)) | → | F |
| eqt(pending, cons(H2, T2)) | → | F | | eqt(pending, tuple(H2, T2)) | → | F |
| eqt(pending, tuplenil(H2)) | → | F | | eqt(release, nil) | → | F |
| eqt(release, a) | → | F | | eqt(release, excl) | → | F |
| eqt(release, false) | → | F | | eqt(release, lock) | → | F |
| eqt(release, locker) | → | F | | eqt(release, mcrlrecord) | → | F |
| eqt(release, ok) | → | F | | eqt(request, mcrlrecord) | → | F |
| eqt(request, ok) | → | F | | eqt(request, pending) | → | F |
| eqt(request, release) | → | F | | eqt(request, request) | → | T |
| eqt(request, resource) | → | F | | eqt(request, tag) | → | F |
| eqt(request, true) | → | F | | eqt(request, undefined) | → | F |
| eqt(request, pid(N2)) | → | F | | eqt(request, int(N2)) | → | F |
| eqt(request, cons(H2, T2)) | → | F | | eqt(request, tuple(H2, T2)) | → | F |
| eqt(request, tuplenil(H2)) | → | F | | eqt(resource, nil) | → | F |
| eqt(resource, a) | → | F | | eqt(resource, excl) | → | F |
| eqt(resource, false) | → | F | | eqt(resource, lock) | → | F |
| eqt(resource, locker) | → | F | | eqt(resource, mcrlrecord) | → | F |
| eqt(resource, ok) | → | F | | eqt(resource, pending) | → | F |
| eqt(resource, release) | → | F | | eqt(resource, request) | → | F |
| eqt(resource, resource) | → | T | | eqt(resource, tag) | → | F |
| eqt(resource, true) | → | F | | eqt(resource, undefined) | → | F |
| eqt(resource, pid(N2)) | → | F | | eqt(resource, int(N2)) | → | F |
| eqt(resource, cons(H2, T2)) | → | F | | eqt(resource, tuple(H2, T2)) | → | F |
| eqt(resource, tuplenil(H2)) | → | F | | eqt(tag, nil) | → | F |
| eqt(tag, a) | → | F | | eqt(tag, excl) | → | F |
| eqt(tag, false) | → | F | | eqt(tag, lock) | → | F |
| eqt(tag, locker) | → | F | | eqt(tag, mcrlrecord) | → | F |
| eqt(tag, ok) | → | F | | eqt(tag, pending) | → | F |
| eqt(tag, release) | → | F | | eqt(tag, request) | → | F |
| eqt(tag, resource) | → | F | | eqt(tag, tag) | → | T |
| eqt(tag, true) | → | F | | eqt(tag, undefined) | → | F |
| eqt(tag, pid(N2)) | → | F | | eqt(tag, int(N2)) | → | F |
| eqt(tag, cons(H2, T2)) | → | F | | eqt(tag, tuple(H2, T2)) | → | F |
| eqt(tag, tuplenil(H2)) | → | F | | eqt(true, nil) | → | F |
| eqt(true, a) | → | F | | eqt(true, excl) | → | F |
| eqt(true, false) | → | F | | eqt(true, lock) | → | F |
| eqt(true, locker) | → | F | | eqt(true, mcrlrecord) | → | F |
| eqt(true, ok) | → | F | | eqt(true, pending) | → | F |
| eqt(true, release) | → | F | | eqt(true, request) | → | F |
| eqt(true, resource) | → | F | | eqt(true, tag) | → | F |
| eqt(true, true) | → | T | | eqt(true, undefined) | → | F |
| eqt(true, pid(N2)) | → | F | | eqt(true, int(N2)) | → | F |
| eqt(true, cons(H2, T2)) | → | F | | eqt(true, tuple(H2, T2)) | → | F |
| eqt(true, tuplenil(H2)) | → | F | | eqt(undefined, nil) | → | F |
| eqt(undefined, a) | → | F | | eqt(undefined, tuplenil(H2)) | → | F |
| eqt(pid(N1), nil) | → | F | | eqt(pid(N1), a) | → | F |
| eqt(pid(N1), excl) | → | F | | eqt(pid(N1), false) | → | F |
| eqt(pid(N1), lock) | → | F | | eqt(pid(N1), locker) | → | F |
| eqt(pid(N1), mcrlrecord) | → | F | | eqt(pid(N1), ok) | → | F |
| eqt(pid(N1), pending) | → | F | | eqt(pid(N1), release) | → | F |
| eqt(pid(N1), request) | → | F | | eqt(pid(N1), resource) | → | F |
| eqt(pid(N1), tag) | → | F | | eqt(pid(N1), true) | → | F |
| eqt(pid(N1), undefined) | → | F | | eqt(pid(N1), pid(N2)) | → | eqt(N1, N2) |
| eqt(pid(N1), int(N2)) | → | F | | eqt(pid(N1), cons(H2, T2)) | → | F |
| eqt(pid(N1), tuple(H2, T2)) | → | F | | eqt(pid(N1), tuplenil(H2)) | → | F |
| eqt(int(N1), nil) | → | F | | eqt(int(N1), a) | → | F |
| eqt(int(N1), excl) | → | F | | eqt(int(N1), false) | → | F |
| eqt(int(N1), lock) | → | F | | eqt(int(N1), locker) | → | F |
| eqt(int(N1), mcrlrecord) | → | F | | eqt(int(N1), ok) | → | F |
| eqt(int(N1), pending) | → | F | | eqt(int(N1), release) | → | F |
| eqt(int(N1), request) | → | F | | eqt(int(N1), resource) | → | F |
| eqt(int(N1), tag) | → | F | | eqt(int(N1), true) | → | F |
| eqt(int(N1), undefined) | → | F | | eqt(cons(H1, T1), resource) | → | F |
| eqt(cons(H1, T1), tag) | → | F | | eqt(cons(H1, T1), true) | → | F |
| eqt(cons(H1, T1), undefined) | → | F | | eqt(cons(H1, T1), pid(N2)) | → | F |
| eqt(cons(H1, T1), int(N2)) | → | F | | eqt(cons(H1, T1), cons(H2, T2)) | → | and(eqt(H1, H2), eqt(T1, T2)) |
| eqt(cons(H1, T1), tuple(H2, T2)) | → | F | | eqt(cons(H1, T1), tuplenil(H2)) | → | F |
| eqt(tuple(H1, T1), nil) | → | F | | eqt(tuple(H1, T1), a) | → | F |
| eqt(tuple(H1, T1), excl) | → | F | | eqt(tuple(H1, T1), false) | → | F |
| eqt(tuple(H1, T1), lock) | → | F | | eqt(tuple(H1, T1), locker) | → | F |
| eqt(tuple(H1, T1), mcrlrecord) | → | F | | eqt(tuple(H1, T1), ok) | → | F |
| eqt(tuple(H1, T1), pending) | → | F | | eqt(tuple(H1, T1), release) | → | F |
| eqt(tuple(H1, T1), request) | → | F | | eqt(tuple(H1, T1), resource) | → | F |
| eqt(tuple(H1, T1), tag) | → | F | | eqt(tuple(H1, T1), true) | → | F |
| eqt(tuple(H1, T1), undefined) | → | F | | eqt(tuple(H1, T1), pid(N2)) | → | F |
| eqt(tuple(H1, T1), int(N2)) | → | F | | eqt(tuple(H1, T1), cons(H2, T2)) | → | F |
| eqt(tuple(H1, T1), tuple(H2, T2)) | → | and(eqt(H1, H2), eqt(T1, T2)) | | eqt(tuple(H1, T1), tuplenil(H2)) | → | F |
| eqt(tuplenil(H1), nil) | → | F | | eqt(tuplenil(H1), a) | → | F |
| eqt(tuplenil(H1), excl) | → | F | | eqt(tuplenil(H1), false) | → | F |
| eqt(tuplenil(H1), lock) | → | F | | eqt(tuplenil(H1), locker) | → | F |
| eqt(tuplenil(H1), mcrlrecord) | → | F | | eqt(tuplenil(H1), ok) | → | F |
| eqt(tuplenil(H1), pending) | → | F | | eqt(tuplenil(H1), release) | → | F |
| eqt(tuplenil(H1), request) | → | F | | eqt(tuplenil(H1), resource) | → | F |
| eqt(tuplenil(H1), tag) | → | F | | eqt(tuplenil(H1), true) | → | F |
| eqt(tuplenil(H1), undefined) | → | F | | eqt(tuplenil(H1), pid(N2)) | → | F |
| eqt(tuplenil(H1), int(N2)) | → | F | | eqt(tuplenil(H1), cons(H2, T2)) | → | F |
| eqt(tuplenil(H1), tuple(H2, T2)) | → | F | | eqt(tuplenil(H1), tuplenil(H2)) | → | eqt(H1, H2) |
| element(int(s(0)), tuplenil(T1)) | → | T1 | | element(int(s(0)), tuple(T1, T2)) | → | T1 |
| element(int(s(s(N1))), tuple(T1, T2)) | → | element(int(s(N1)), T2) | | record_new(lock) | → | tuple(mcrlrecord, tuple(lock, tuple(undefined, tuple(nil, tuplenil(nil))))) |
| record_extract(tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2))))), lock, resource) | → | tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2))))) | | record_update(tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2))))), lock, pending, NewF) | → | tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(NewF))))) |
| record_updates(Record, Name, nil) | → | Record | | record_updates(Record, Name, cons(tuple(Field, tuplenil(NewF)), Fields)) | → | record_updates(record_update(Record, Name, Field, NewF), Name, Fields) |
| locker2_map_promote_pending(nil, Pending) | → | nil | | locker2_map_promote_pending(cons(Lock, Locks), Pending) | → | cons(locker2_promote_pending(Lock, Pending), locker2_map_promote_pending(Locks, Pending)) |
| locker2_map_claim_lock(nil, Resources, Client) | → | nil | | locker2_map_claim_lock(cons(Lock, Locks), Resources, Client) | → | cons(locker2_claim_lock(Lock, Resources, Client), locker2_map_claim_lock(Locks, Resources, Client)) |
| locker2_map_add_pending(nil, Resources, Client) | → | nil | | locker2_promote_pending(Lock, Client) | → | case0(Client, Lock, record_extract(Lock, lock, pending)) |
| case0(Client, Lock, cons(Client, Pendings)) | → | record_updates(Lock, lock, cons(tuple(excl, tuplenil(Client)), cons(tuple(pending, tuplenil(Pendings)), nil))) | | case0(Client, Lock, MCRLFree0) | → | Lock |
| locker2_remove_pending(Lock, Client) | → | record_updates(Lock, lock, cons(tuple(pending, tuplenil(subtract(record_extract(Lock, lock, pending), cons(Client, nil)))), nil)) | | locker2_add_pending(Lock, Resources, Client) | → | case1(Client, Resources, Lock, member(record_extract(Lock, lock, resource), Resources)) |
| case1(Client, Resources, Lock, true) | → | record_updates(Lock, lock, cons(tuple(pending, tuplenil(append(record_extract(Lock, lock, pending), cons(Client, nil)))), nil)) | | case1(Client, Resources, Lock, false) | → | Lock |
| locker2_release_lock(Lock, Client) | → | case2(Client, Lock, gen_modtageq(Client, record_extract(Lock, lock, excl))) | | case2(Client, Lock, true) | → | record_updates(Lock, lock, cons(tuple(excllock, excl), nil)) |
| case4(Client, Lock, MCRLFree1) | → | false | | locker2_obtainables(nil, Client) | → | true |
| locker2_obtainables(cons(Lock, Locks), Client) | → | case5(Client, Locks, Lock, member(Client, record_extract(Lock, lock, pending))) | | case5(Client, Locks, Lock, true) | → | andt(locker2_obtainable(Lock, Client), locker2_obtainables(Locks, Client)) |
| case5(Client, Locks, Lock, false) | → | locker2_obtainables(Locks, Client) | | locker2_check_available(Resource, nil) | → | false |
| locker2_check_available(Resource, cons(Lock, Locks)) | → | case6(Locks, Lock, Resource, equal(Resource, record_extract(Lock, lock, resource))) | | case6(Locks, Lock, Resource, true) | → | andt(equal(record_extract(Lock, lock, excl), nil), equal(record_extract(Lock, lock, pending), nil)) |
| case6(Locks, Lock, Resource, false) | → | locker2_check_available(Resource, Locks) | | locker2_check_availables(nil, Locks) | → | true |
| locker2_check_availables(cons(Resource, Resources), Locks) | → | andt(locker2_check_available(Resource, Locks), locker2_check_availables(Resources, Locks)) | | locker2_adduniq(nil, List) | → | List |
| append(cons(Head, Tail), List) | → | cons(Head, append(Tail, List)) | | subtract(List, nil) | → | List |
| subtract(List, cons(Head, Tail)) | → | subtract(delete(Head, List), Tail) | | delete(E, nil) | → | nil |
| delete(E, cons(Head, Tail)) | → | case8(Tail, Head, E, equal(E, Head)) | | case8(Tail, Head, E, true) | → | Tail |
| case8(Tail, Head, E, false) | → | cons(Head, delete(E, Tail)) | | gen_tag(Pid) | → | tuple(Pid, tuplenil(tag)) |
| gen_modtageq(Client1, Client2) | → | equal(Client1, Client2) | | member(E, nil) | → | false |
| member(E, cons(Head, Tail)) | → | case9(Tail, Head, E, equal(E, Head)) | | case9(Tail, Head, E, true) | → | true |
| case9(Tail, Head, E, false) | → | member(E, Tail) | | eqs(empty, empty) | → | T |
| eqs(empty, stack(E2, S2)) | → | F | | eqs(stack(E1, S1), empty) | → | F |
| eqs(stack(E1, S1), stack(E2, S2)) | → | and(eqt(E1, E2), eqs(S1, S2)) | | pushs(E1, S1) | → | stack(E1, S1) |
| pops(stack(E1, S1)) | → | S1 | | tops(stack(E1, S1)) | → | E1 |
| istops(E1, empty) | → | F | | istops(E1, stack(E2, S1)) | → | eqt(E1, E2) |
| eqc(nocalls, nocalls) | → | T | | eqc(nocalls, calls(E2, S2, CS2)) | → | F |
| eqc(calls(E1, S1, CS1), nocalls) | → | F | | eqc(calls(E1, S1, CS1), calls(E2, S2, CS2)) | → | and(eqt(E1, E2), and(eqs(S1, S2), eqc(CS1, CS2))) |
| push(E1, E2, nocalls) | → | calls(E1, stack(E2, empty), nocalls) | | push(E1, E2, calls(E3, S1, CS1)) | → | push1(E1, E2, E3, S1, CS1, eqt(E1, E3)) |
| push1(E1, E2, E3, S1, CS1, T) | → | calls(E3, pushs(E2, S1), CS1) |
Original Signature
Termination of terms over the following signature is verified: tuplenil, record_new, tuple, tag, gen_tag, imp, locker2_map_promote_pending, pops, locker2_check_availables, mcrlrecord, pending, request, empty, false, ok, istops, locker2_add_pending, andt, case2, append, element, case1, case0, tops, push1, case6, case5, or, int, case4, record_extract, locker, case9, case8, locker2_map_add_pending, calls, eqc, and, not, 0, locker2_promote_pending, locker2_claim_lock, locker2_adduniq, stack, release, locker2_obtainables, F, locker2_remove_pending, push, T, gen_modtageq, record_update, undefined, if, record_updates, eqt, excllock, delete, eqs, cons, member, locker2_map_claim_lock, locker2_obtainable, a, pushs, resource, lock, true, locker2_release_lock, pid, equal, subtract, locker2_check_available, s, excl, nil, eq, nocalls
Strategy
Projection
The following projection was used:
Thus, the following dependency pairs are removed:
| subtract#(List, cons(Head, Tail)) | → | subtract#(delete(Head, List), Tail) |
Problem 5: SubtermCriterion
Dependency Pair Problem
Dependency Pairs
| locker2_map_claim_lock#(cons(Lock, Locks), Resources, Client) | → | locker2_map_claim_lock#(Locks, Resources, Client) |
Rewrite Rules
| or(T, T) | → | T | | or(F, T) | → | T |
| or(T, F) | → | T | | or(F, F) | → | F |
| and(T, B) | → | B | | and(B, T) | → | B |
| and(F, B) | → | F | | and(B, F) | → | F |
| imp(T, B) | → | B | | imp(F, B) | → | T |
| not(T) | → | F | | not(F) | → | T |
| if(T, B1, B2) | → | B1 | | if(F, B1, B2) | → | B2 |
| eq(T, T) | → | T | | eq(F, F) | → | T |
| eq(T, F) | → | F | | eq(F, T) | → | F |
| eqt(nil, undefined) | → | F | | eqt(nil, pid(N2)) | → | F |
| eqt(nil, int(N2)) | → | F | | eqt(nil, cons(H2, T2)) | → | F |
| eqt(nil, tuple(H2, T2)) | → | F | | eqt(nil, tuplenil(H2)) | → | F |
| eqt(a, nil) | → | F | | eqt(a, a) | → | T |
| eqt(a, excl) | → | F | | eqt(a, false) | → | F |
| eqt(a, lock) | → | F | | eqt(a, locker) | → | F |
| eqt(a, mcrlrecord) | → | F | | eqt(a, ok) | → | F |
| eqt(a, pending) | → | F | | eqt(a, release) | → | F |
| eqt(a, request) | → | F | | eqt(a, resource) | → | F |
| eqt(a, tag) | → | F | | eqt(a, true) | → | F |
| eqt(a, undefined) | → | F | | eqt(a, pid(N2)) | → | F |
| eqt(a, int(N2)) | → | F | | eqt(a, cons(H2, T2)) | → | F |
| eqt(a, tuple(H2, T2)) | → | F | | eqt(a, tuplenil(H2)) | → | F |
| eqt(excl, nil) | → | F | | eqt(excl, a) | → | F |
| eqt(excl, excl) | → | T | | eqt(excl, false) | → | F |
| eqt(excl, lock) | → | F | | eqt(excl, locker) | → | F |
| eqt(excl, mcrlrecord) | → | F | | eqt(excl, ok) | → | F |
| eqt(excl, pending) | → | F | | eqt(excl, release) | → | F |
| eqt(excl, request) | → | F | | eqt(excl, resource) | → | F |
| eqt(excl, tag) | → | F | | eqt(excl, true) | → | F |
| eqt(excl, undefined) | → | F | | eqt(excl, pid(N2)) | → | F |
| eqt(excl, eqt(false, int(N2))) | → | F | | eqt(false, cons(H2, T2)) | → | F |
| eqt(false, tuple(H2, T2)) | → | F | | eqt(false, tuplenil(H2)) | → | F |
| eqt(lock, nil) | → | F | | eqt(lock, a) | → | F |
| eqt(lock, excl) | → | F | | eqt(lock, false) | → | F |
| eqt(lock, lock) | → | T | | eqt(lock, locker) | → | F |
| eqt(lock, mcrlrecord) | → | F | | eqt(lock, ok) | → | F |
| eqt(lock, pending) | → | F | | eqt(lock, release) | → | F |
| eqt(lock, request) | → | F | | eqt(lock, resource) | → | F |
| eqt(lock, tag) | → | F | | eqt(lock, true) | → | F |
| eqt(lock, undefined) | → | F | | eqt(lock, pid(N2)) | → | F |
| eqt(lock, int(N2)) | → | F | | eqt(lock, cons(H2, T2)) | → | F |
| eqt(lock, tuple(H2, T2)) | → | F | | eqt(lock, tuplenil(H2)) | → | F |
| eqt(locker, nil) | → | F | | eqt(locker, a) | → | F |
| eqt(locker, excl) | → | F | | eqt(locker, false) | → | F |
| eqt(locker, lock) | → | F | | eqt(locker, locker) | → | T |
| eqt(locker, mcrlrecord) | → | F | | eqt(locker, ok) | → | F |
| eqt(locker, pending) | → | F | | eqt(locker, release) | → | F |
| eqt(locker, request) | → | F | | eqt(locker, resource) | → | F |
| eqt(locker, tag) | → | F | | eqt(locker, true) | → | F |
| eqt(locker, undefined) | → | F | | eqt(locker, pid(N2)) | → | F |
| eqt(locker, int(N2)) | → | F | | eqt(locker, cons(H2, T2)) | → | F |
| eqt(locker, tuple(H2, T2)) | → | F | | eqt(locker, tuplenil(H2)) | → | F |
| eqt(mcrlrecord, nil) | → | F | | eqt(mcrlrecord, a) | → | F |
| eqt(mcrlrecord, excl) | → | F | | eqt(mcrlrecord, false) | → | F |
| eqt(mcrlrecord, lock) | → | F | | eqt(mcrlrecord, locker) | → | F |
| eqt(mcrlrecord, mcrlrecord) | → | T | | eqt(mcrlrecord, ok) | → | F |
| eqt(mcrlrecord, pending) | → | F | | eqt(mcrlrecord, release) | → | F |
| eqt(mcrlrecord, request) | → | F | | eqt(mcrlrecord, resource) | → | F |
| eqt(ok, resource) | → | F | | eqt(ok, tag) | → | F |
| eqt(ok, true) | → | F | | eqt(ok, undefined) | → | F |
| eqt(ok, pid(N2)) | → | F | | eqt(ok, int(N2)) | → | F |
| eqt(ok, cons(H2, T2)) | → | F | | eqt(ok, tuple(H2, T2)) | → | F |
| eqt(ok, tuplenil(H2)) | → | F | | eqt(pending, nil) | → | F |
| eqt(pending, a) | → | F | | eqt(pending, excl) | → | F |
| eqt(pending, false) | → | F | | eqt(pending, lock) | → | F |
| eqt(pending, locker) | → | F | | eqt(pending, mcrlrecord) | → | F |
| eqt(pending, ok) | → | F | | eqt(pending, pending) | → | T |
| eqt(pending, release) | → | F | | eqt(pending, request) | → | F |
| eqt(pending, resource) | → | F | | eqt(pending, tag) | → | F |
| eqt(pending, true) | → | F | | eqt(pending, undefined) | → | F |
| eqt(pending, pid(N2)) | → | F | | eqt(pending, int(N2)) | → | F |
| eqt(pending, cons(H2, T2)) | → | F | | eqt(pending, tuple(H2, T2)) | → | F |
| eqt(pending, tuplenil(H2)) | → | F | | eqt(release, nil) | → | F |
| eqt(release, a) | → | F | | eqt(release, excl) | → | F |
| eqt(release, false) | → | F | | eqt(release, lock) | → | F |
| eqt(release, locker) | → | F | | eqt(release, mcrlrecord) | → | F |
| eqt(release, ok) | → | F | | eqt(request, mcrlrecord) | → | F |
| eqt(request, ok) | → | F | | eqt(request, pending) | → | F |
| eqt(request, release) | → | F | | eqt(request, request) | → | T |
| eqt(request, resource) | → | F | | eqt(request, tag) | → | F |
| eqt(request, true) | → | F | | eqt(request, undefined) | → | F |
| eqt(request, pid(N2)) | → | F | | eqt(request, int(N2)) | → | F |
| eqt(request, cons(H2, T2)) | → | F | | eqt(request, tuple(H2, T2)) | → | F |
| eqt(request, tuplenil(H2)) | → | F | | eqt(resource, nil) | → | F |
| eqt(resource, a) | → | F | | eqt(resource, excl) | → | F |
| eqt(resource, false) | → | F | | eqt(resource, lock) | → | F |
| eqt(resource, locker) | → | F | | eqt(resource, mcrlrecord) | → | F |
| eqt(resource, ok) | → | F | | eqt(resource, pending) | → | F |
| eqt(resource, release) | → | F | | eqt(resource, request) | → | F |
| eqt(resource, resource) | → | T | | eqt(resource, tag) | → | F |
| eqt(resource, true) | → | F | | eqt(resource, undefined) | → | F |
| eqt(resource, pid(N2)) | → | F | | eqt(resource, int(N2)) | → | F |
| eqt(resource, cons(H2, T2)) | → | F | | eqt(resource, tuple(H2, T2)) | → | F |
| eqt(resource, tuplenil(H2)) | → | F | | eqt(tag, nil) | → | F |
| eqt(tag, a) | → | F | | eqt(tag, excl) | → | F |
| eqt(tag, false) | → | F | | eqt(tag, lock) | → | F |
| eqt(tag, locker) | → | F | | eqt(tag, mcrlrecord) | → | F |
| eqt(tag, ok) | → | F | | eqt(tag, pending) | → | F |
| eqt(tag, release) | → | F | | eqt(tag, request) | → | F |
| eqt(tag, resource) | → | F | | eqt(tag, tag) | → | T |
| eqt(tag, true) | → | F | | eqt(tag, undefined) | → | F |
| eqt(tag, pid(N2)) | → | F | | eqt(tag, int(N2)) | → | F |
| eqt(tag, cons(H2, T2)) | → | F | | eqt(tag, tuple(H2, T2)) | → | F |
| eqt(tag, tuplenil(H2)) | → | F | | eqt(true, nil) | → | F |
| eqt(true, a) | → | F | | eqt(true, excl) | → | F |
| eqt(true, false) | → | F | | eqt(true, lock) | → | F |
| eqt(true, locker) | → | F | | eqt(true, mcrlrecord) | → | F |
| eqt(true, ok) | → | F | | eqt(true, pending) | → | F |
| eqt(true, release) | → | F | | eqt(true, request) | → | F |
| eqt(true, resource) | → | F | | eqt(true, tag) | → | F |
| eqt(true, true) | → | T | | eqt(true, undefined) | → | F |
| eqt(true, pid(N2)) | → | F | | eqt(true, int(N2)) | → | F |
| eqt(true, cons(H2, T2)) | → | F | | eqt(true, tuple(H2, T2)) | → | F |
| eqt(true, tuplenil(H2)) | → | F | | eqt(undefined, nil) | → | F |
| eqt(undefined, a) | → | F | | eqt(undefined, tuplenil(H2)) | → | F |
| eqt(pid(N1), nil) | → | F | | eqt(pid(N1), a) | → | F |
| eqt(pid(N1), excl) | → | F | | eqt(pid(N1), false) | → | F |
| eqt(pid(N1), lock) | → | F | | eqt(pid(N1), locker) | → | F |
| eqt(pid(N1), mcrlrecord) | → | F | | eqt(pid(N1), ok) | → | F |
| eqt(pid(N1), pending) | → | F | | eqt(pid(N1), release) | → | F |
| eqt(pid(N1), request) | → | F | | eqt(pid(N1), resource) | → | F |
| eqt(pid(N1), tag) | → | F | | eqt(pid(N1), true) | → | F |
| eqt(pid(N1), undefined) | → | F | | eqt(pid(N1), pid(N2)) | → | eqt(N1, N2) |
| eqt(pid(N1), int(N2)) | → | F | | eqt(pid(N1), cons(H2, T2)) | → | F |
| eqt(pid(N1), tuple(H2, T2)) | → | F | | eqt(pid(N1), tuplenil(H2)) | → | F |
| eqt(int(N1), nil) | → | F | | eqt(int(N1), a) | → | F |
| eqt(int(N1), excl) | → | F | | eqt(int(N1), false) | → | F |
| eqt(int(N1), lock) | → | F | | eqt(int(N1), locker) | → | F |
| eqt(int(N1), mcrlrecord) | → | F | | eqt(int(N1), ok) | → | F |
| eqt(int(N1), pending) | → | F | | eqt(int(N1), release) | → | F |
| eqt(int(N1), request) | → | F | | eqt(int(N1), resource) | → | F |
| eqt(int(N1), tag) | → | F | | eqt(int(N1), true) | → | F |
| eqt(int(N1), undefined) | → | F | | eqt(cons(H1, T1), resource) | → | F |
| eqt(cons(H1, T1), tag) | → | F | | eqt(cons(H1, T1), true) | → | F |
| eqt(cons(H1, T1), undefined) | → | F | | eqt(cons(H1, T1), pid(N2)) | → | F |
| eqt(cons(H1, T1), int(N2)) | → | F | | eqt(cons(H1, T1), cons(H2, T2)) | → | and(eqt(H1, H2), eqt(T1, T2)) |
| eqt(cons(H1, T1), tuple(H2, T2)) | → | F | | eqt(cons(H1, T1), tuplenil(H2)) | → | F |
| eqt(tuple(H1, T1), nil) | → | F | | eqt(tuple(H1, T1), a) | → | F |
| eqt(tuple(H1, T1), excl) | → | F | | eqt(tuple(H1, T1), false) | → | F |
| eqt(tuple(H1, T1), lock) | → | F | | eqt(tuple(H1, T1), locker) | → | F |
| eqt(tuple(H1, T1), mcrlrecord) | → | F | | eqt(tuple(H1, T1), ok) | → | F |
| eqt(tuple(H1, T1), pending) | → | F | | eqt(tuple(H1, T1), release) | → | F |
| eqt(tuple(H1, T1), request) | → | F | | eqt(tuple(H1, T1), resource) | → | F |
| eqt(tuple(H1, T1), tag) | → | F | | eqt(tuple(H1, T1), true) | → | F |
| eqt(tuple(H1, T1), undefined) | → | F | | eqt(tuple(H1, T1), pid(N2)) | → | F |
| eqt(tuple(H1, T1), int(N2)) | → | F | | eqt(tuple(H1, T1), cons(H2, T2)) | → | F |
| eqt(tuple(H1, T1), tuple(H2, T2)) | → | and(eqt(H1, H2), eqt(T1, T2)) | | eqt(tuple(H1, T1), tuplenil(H2)) | → | F |
| eqt(tuplenil(H1), nil) | → | F | | eqt(tuplenil(H1), a) | → | F |
| eqt(tuplenil(H1), excl) | → | F | | eqt(tuplenil(H1), false) | → | F |
| eqt(tuplenil(H1), lock) | → | F | | eqt(tuplenil(H1), locker) | → | F |
| eqt(tuplenil(H1), mcrlrecord) | → | F | | eqt(tuplenil(H1), ok) | → | F |
| eqt(tuplenil(H1), pending) | → | F | | eqt(tuplenil(H1), release) | → | F |
| eqt(tuplenil(H1), request) | → | F | | eqt(tuplenil(H1), resource) | → | F |
| eqt(tuplenil(H1), tag) | → | F | | eqt(tuplenil(H1), true) | → | F |
| eqt(tuplenil(H1), undefined) | → | F | | eqt(tuplenil(H1), pid(N2)) | → | F |
| eqt(tuplenil(H1), int(N2)) | → | F | | eqt(tuplenil(H1), cons(H2, T2)) | → | F |
| eqt(tuplenil(H1), tuple(H2, T2)) | → | F | | eqt(tuplenil(H1), tuplenil(H2)) | → | eqt(H1, H2) |
| element(int(s(0)), tuplenil(T1)) | → | T1 | | element(int(s(0)), tuple(T1, T2)) | → | T1 |
| element(int(s(s(N1))), tuple(T1, T2)) | → | element(int(s(N1)), T2) | | record_new(lock) | → | tuple(mcrlrecord, tuple(lock, tuple(undefined, tuple(nil, tuplenil(nil))))) |
| record_extract(tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2))))), lock, resource) | → | tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2))))) | | record_update(tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2))))), lock, pending, NewF) | → | tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(NewF))))) |
| record_updates(Record, Name, nil) | → | Record | | record_updates(Record, Name, cons(tuple(Field, tuplenil(NewF)), Fields)) | → | record_updates(record_update(Record, Name, Field, NewF), Name, Fields) |
| locker2_map_promote_pending(nil, Pending) | → | nil | | locker2_map_promote_pending(cons(Lock, Locks), Pending) | → | cons(locker2_promote_pending(Lock, Pending), locker2_map_promote_pending(Locks, Pending)) |
| locker2_map_claim_lock(nil, Resources, Client) | → | nil | | locker2_map_claim_lock(cons(Lock, Locks), Resources, Client) | → | cons(locker2_claim_lock(Lock, Resources, Client), locker2_map_claim_lock(Locks, Resources, Client)) |
| locker2_map_add_pending(nil, Resources, Client) | → | nil | | locker2_promote_pending(Lock, Client) | → | case0(Client, Lock, record_extract(Lock, lock, pending)) |
| case0(Client, Lock, cons(Client, Pendings)) | → | record_updates(Lock, lock, cons(tuple(excl, tuplenil(Client)), cons(tuple(pending, tuplenil(Pendings)), nil))) | | case0(Client, Lock, MCRLFree0) | → | Lock |
| locker2_remove_pending(Lock, Client) | → | record_updates(Lock, lock, cons(tuple(pending, tuplenil(subtract(record_extract(Lock, lock, pending), cons(Client, nil)))), nil)) | | locker2_add_pending(Lock, Resources, Client) | → | case1(Client, Resources, Lock, member(record_extract(Lock, lock, resource), Resources)) |
| case1(Client, Resources, Lock, true) | → | record_updates(Lock, lock, cons(tuple(pending, tuplenil(append(record_extract(Lock, lock, pending), cons(Client, nil)))), nil)) | | case1(Client, Resources, Lock, false) | → | Lock |
| locker2_release_lock(Lock, Client) | → | case2(Client, Lock, gen_modtageq(Client, record_extract(Lock, lock, excl))) | | case2(Client, Lock, true) | → | record_updates(Lock, lock, cons(tuple(excllock, excl), nil)) |
| case4(Client, Lock, MCRLFree1) | → | false | | locker2_obtainables(nil, Client) | → | true |
| locker2_obtainables(cons(Lock, Locks), Client) | → | case5(Client, Locks, Lock, member(Client, record_extract(Lock, lock, pending))) | | case5(Client, Locks, Lock, true) | → | andt(locker2_obtainable(Lock, Client), locker2_obtainables(Locks, Client)) |
| case5(Client, Locks, Lock, false) | → | locker2_obtainables(Locks, Client) | | locker2_check_available(Resource, nil) | → | false |
| locker2_check_available(Resource, cons(Lock, Locks)) | → | case6(Locks, Lock, Resource, equal(Resource, record_extract(Lock, lock, resource))) | | case6(Locks, Lock, Resource, true) | → | andt(equal(record_extract(Lock, lock, excl), nil), equal(record_extract(Lock, lock, pending), nil)) |
| case6(Locks, Lock, Resource, false) | → | locker2_check_available(Resource, Locks) | | locker2_check_availables(nil, Locks) | → | true |
| locker2_check_availables(cons(Resource, Resources), Locks) | → | andt(locker2_check_available(Resource, Locks), locker2_check_availables(Resources, Locks)) | | locker2_adduniq(nil, List) | → | List |
| append(cons(Head, Tail), List) | → | cons(Head, append(Tail, List)) | | subtract(List, nil) | → | List |
| subtract(List, cons(Head, Tail)) | → | subtract(delete(Head, List), Tail) | | delete(E, nil) | → | nil |
| delete(E, cons(Head, Tail)) | → | case8(Tail, Head, E, equal(E, Head)) | | case8(Tail, Head, E, true) | → | Tail |
| case8(Tail, Head, E, false) | → | cons(Head, delete(E, Tail)) | | gen_tag(Pid) | → | tuple(Pid, tuplenil(tag)) |
| gen_modtageq(Client1, Client2) | → | equal(Client1, Client2) | | member(E, nil) | → | false |
| member(E, cons(Head, Tail)) | → | case9(Tail, Head, E, equal(E, Head)) | | case9(Tail, Head, E, true) | → | true |
| case9(Tail, Head, E, false) | → | member(E, Tail) | | eqs(empty, empty) | → | T |
| eqs(empty, stack(E2, S2)) | → | F | | eqs(stack(E1, S1), empty) | → | F |
| eqs(stack(E1, S1), stack(E2, S2)) | → | and(eqt(E1, E2), eqs(S1, S2)) | | pushs(E1, S1) | → | stack(E1, S1) |
| pops(stack(E1, S1)) | → | S1 | | tops(stack(E1, S1)) | → | E1 |
| istops(E1, empty) | → | F | | istops(E1, stack(E2, S1)) | → | eqt(E1, E2) |
| eqc(nocalls, nocalls) | → | T | | eqc(nocalls, calls(E2, S2, CS2)) | → | F |
| eqc(calls(E1, S1, CS1), nocalls) | → | F | | eqc(calls(E1, S1, CS1), calls(E2, S2, CS2)) | → | and(eqt(E1, E2), and(eqs(S1, S2), eqc(CS1, CS2))) |
| push(E1, E2, nocalls) | → | calls(E1, stack(E2, empty), nocalls) | | push(E1, E2, calls(E3, S1, CS1)) | → | push1(E1, E2, E3, S1, CS1, eqt(E1, E3)) |
| push1(E1, E2, E3, S1, CS1, T) | → | calls(E3, pushs(E2, S1), CS1) |
Original Signature
Termination of terms over the following signature is verified: tuplenil, record_new, tuple, tag, gen_tag, imp, locker2_map_promote_pending, pops, locker2_check_availables, mcrlrecord, pending, request, empty, false, ok, istops, locker2_add_pending, andt, case2, append, element, case1, case0, tops, push1, case6, case5, or, int, case4, record_extract, locker, case9, case8, locker2_map_add_pending, calls, eqc, and, not, 0, locker2_promote_pending, locker2_claim_lock, locker2_adduniq, stack, release, locker2_obtainables, F, locker2_remove_pending, push, T, gen_modtageq, record_update, undefined, if, record_updates, eqt, excllock, delete, eqs, cons, member, locker2_map_claim_lock, locker2_obtainable, a, pushs, resource, lock, true, locker2_release_lock, pid, equal, subtract, locker2_check_available, s, excl, nil, eq, nocalls
Strategy
Projection
The following projection was used:
- π (locker2_map_claim_lock#): 1
Thus, the following dependency pairs are removed:
| locker2_map_claim_lock#(cons(Lock, Locks), Resources, Client) | → | locker2_map_claim_lock#(Locks, Resources, Client) |
Problem 6: SubtermCriterion
Dependency Pair Problem
Dependency Pairs
| case5#(Client, Locks, Lock, true) | → | locker2_obtainables#(Locks, Client) | | case5#(Client, Locks, Lock, false) | → | locker2_obtainables#(Locks, Client) |
| locker2_obtainables#(cons(Lock, Locks), Client) | → | case5#(Client, Locks, Lock, member(Client, record_extract(Lock, lock, pending))) |
Rewrite Rules
| or(T, T) | → | T | | or(F, T) | → | T |
| or(T, F) | → | T | | or(F, F) | → | F |
| and(T, B) | → | B | | and(B, T) | → | B |
| and(F, B) | → | F | | and(B, F) | → | F |
| imp(T, B) | → | B | | imp(F, B) | → | T |
| not(T) | → | F | | not(F) | → | T |
| if(T, B1, B2) | → | B1 | | if(F, B1, B2) | → | B2 |
| eq(T, T) | → | T | | eq(F, F) | → | T |
| eq(T, F) | → | F | | eq(F, T) | → | F |
| eqt(nil, undefined) | → | F | | eqt(nil, pid(N2)) | → | F |
| eqt(nil, int(N2)) | → | F | | eqt(nil, cons(H2, T2)) | → | F |
| eqt(nil, tuple(H2, T2)) | → | F | | eqt(nil, tuplenil(H2)) | → | F |
| eqt(a, nil) | → | F | | eqt(a, a) | → | T |
| eqt(a, excl) | → | F | | eqt(a, false) | → | F |
| eqt(a, lock) | → | F | | eqt(a, locker) | → | F |
| eqt(a, mcrlrecord) | → | F | | eqt(a, ok) | → | F |
| eqt(a, pending) | → | F | | eqt(a, release) | → | F |
| eqt(a, request) | → | F | | eqt(a, resource) | → | F |
| eqt(a, tag) | → | F | | eqt(a, true) | → | F |
| eqt(a, undefined) | → | F | | eqt(a, pid(N2)) | → | F |
| eqt(a, int(N2)) | → | F | | eqt(a, cons(H2, T2)) | → | F |
| eqt(a, tuple(H2, T2)) | → | F | | eqt(a, tuplenil(H2)) | → | F |
| eqt(excl, nil) | → | F | | eqt(excl, a) | → | F |
| eqt(excl, excl) | → | T | | eqt(excl, false) | → | F |
| eqt(excl, lock) | → | F | | eqt(excl, locker) | → | F |
| eqt(excl, mcrlrecord) | → | F | | eqt(excl, ok) | → | F |
| eqt(excl, pending) | → | F | | eqt(excl, release) | → | F |
| eqt(excl, request) | → | F | | eqt(excl, resource) | → | F |
| eqt(excl, tag) | → | F | | eqt(excl, true) | → | F |
| eqt(excl, undefined) | → | F | | eqt(excl, pid(N2)) | → | F |
| eqt(excl, eqt(false, int(N2))) | → | F | | eqt(false, cons(H2, T2)) | → | F |
| eqt(false, tuple(H2, T2)) | → | F | | eqt(false, tuplenil(H2)) | → | F |
| eqt(lock, nil) | → | F | | eqt(lock, a) | → | F |
| eqt(lock, excl) | → | F | | eqt(lock, false) | → | F |
| eqt(lock, lock) | → | T | | eqt(lock, locker) | → | F |
| eqt(lock, mcrlrecord) | → | F | | eqt(lock, ok) | → | F |
| eqt(lock, pending) | → | F | | eqt(lock, release) | → | F |
| eqt(lock, request) | → | F | | eqt(lock, resource) | → | F |
| eqt(lock, tag) | → | F | | eqt(lock, true) | → | F |
| eqt(lock, undefined) | → | F | | eqt(lock, pid(N2)) | → | F |
| eqt(lock, int(N2)) | → | F | | eqt(lock, cons(H2, T2)) | → | F |
| eqt(lock, tuple(H2, T2)) | → | F | | eqt(lock, tuplenil(H2)) | → | F |
| eqt(locker, nil) | → | F | | eqt(locker, a) | → | F |
| eqt(locker, excl) | → | F | | eqt(locker, false) | → | F |
| eqt(locker, lock) | → | F | | eqt(locker, locker) | → | T |
| eqt(locker, mcrlrecord) | → | F | | eqt(locker, ok) | → | F |
| eqt(locker, pending) | → | F | | eqt(locker, release) | → | F |
| eqt(locker, request) | → | F | | eqt(locker, resource) | → | F |
| eqt(locker, tag) | → | F | | eqt(locker, true) | → | F |
| eqt(locker, undefined) | → | F | | eqt(locker, pid(N2)) | → | F |
| eqt(locker, int(N2)) | → | F | | eqt(locker, cons(H2, T2)) | → | F |
| eqt(locker, tuple(H2, T2)) | → | F | | eqt(locker, tuplenil(H2)) | → | F |
| eqt(mcrlrecord, nil) | → | F | | eqt(mcrlrecord, a) | → | F |
| eqt(mcrlrecord, excl) | → | F | | eqt(mcrlrecord, false) | → | F |
| eqt(mcrlrecord, lock) | → | F | | eqt(mcrlrecord, locker) | → | F |
| eqt(mcrlrecord, mcrlrecord) | → | T | | eqt(mcrlrecord, ok) | → | F |
| eqt(mcrlrecord, pending) | → | F | | eqt(mcrlrecord, release) | → | F |
| eqt(mcrlrecord, request) | → | F | | eqt(mcrlrecord, resource) | → | F |
| eqt(ok, resource) | → | F | | eqt(ok, tag) | → | F |
| eqt(ok, true) | → | F | | eqt(ok, undefined) | → | F |
| eqt(ok, pid(N2)) | → | F | | eqt(ok, int(N2)) | → | F |
| eqt(ok, cons(H2, T2)) | → | F | | eqt(ok, tuple(H2, T2)) | → | F |
| eqt(ok, tuplenil(H2)) | → | F | | eqt(pending, nil) | → | F |
| eqt(pending, a) | → | F | | eqt(pending, excl) | → | F |
| eqt(pending, false) | → | F | | eqt(pending, lock) | → | F |
| eqt(pending, locker) | → | F | | eqt(pending, mcrlrecord) | → | F |
| eqt(pending, ok) | → | F | | eqt(pending, pending) | → | T |
| eqt(pending, release) | → | F | | eqt(pending, request) | → | F |
| eqt(pending, resource) | → | F | | eqt(pending, tag) | → | F |
| eqt(pending, true) | → | F | | eqt(pending, undefined) | → | F |
| eqt(pending, pid(N2)) | → | F | | eqt(pending, int(N2)) | → | F |
| eqt(pending, cons(H2, T2)) | → | F | | eqt(pending, tuple(H2, T2)) | → | F |
| eqt(pending, tuplenil(H2)) | → | F | | eqt(release, nil) | → | F |
| eqt(release, a) | → | F | | eqt(release, excl) | → | F |
| eqt(release, false) | → | F | | eqt(release, lock) | → | F |
| eqt(release, locker) | → | F | | eqt(release, mcrlrecord) | → | F |
| eqt(release, ok) | → | F | | eqt(request, mcrlrecord) | → | F |
| eqt(request, ok) | → | F | | eqt(request, pending) | → | F |
| eqt(request, release) | → | F | | eqt(request, request) | → | T |
| eqt(request, resource) | → | F | | eqt(request, tag) | → | F |
| eqt(request, true) | → | F | | eqt(request, undefined) | → | F |
| eqt(request, pid(N2)) | → | F | | eqt(request, int(N2)) | → | F |
| eqt(request, cons(H2, T2)) | → | F | | eqt(request, tuple(H2, T2)) | → | F |
| eqt(request, tuplenil(H2)) | → | F | | eqt(resource, nil) | → | F |
| eqt(resource, a) | → | F | | eqt(resource, excl) | → | F |
| eqt(resource, false) | → | F | | eqt(resource, lock) | → | F |
| eqt(resource, locker) | → | F | | eqt(resource, mcrlrecord) | → | F |
| eqt(resource, ok) | → | F | | eqt(resource, pending) | → | F |
| eqt(resource, release) | → | F | | eqt(resource, request) | → | F |
| eqt(resource, resource) | → | T | | eqt(resource, tag) | → | F |
| eqt(resource, true) | → | F | | eqt(resource, undefined) | → | F |
| eqt(resource, pid(N2)) | → | F | | eqt(resource, int(N2)) | → | F |
| eqt(resource, cons(H2, T2)) | → | F | | eqt(resource, tuple(H2, T2)) | → | F |
| eqt(resource, tuplenil(H2)) | → | F | | eqt(tag, nil) | → | F |
| eqt(tag, a) | → | F | | eqt(tag, excl) | → | F |
| eqt(tag, false) | → | F | | eqt(tag, lock) | → | F |
| eqt(tag, locker) | → | F | | eqt(tag, mcrlrecord) | → | F |
| eqt(tag, ok) | → | F | | eqt(tag, pending) | → | F |
| eqt(tag, release) | → | F | | eqt(tag, request) | → | F |
| eqt(tag, resource) | → | F | | eqt(tag, tag) | → | T |
| eqt(tag, true) | → | F | | eqt(tag, undefined) | → | F |
| eqt(tag, pid(N2)) | → | F | | eqt(tag, int(N2)) | → | F |
| eqt(tag, cons(H2, T2)) | → | F | | eqt(tag, tuple(H2, T2)) | → | F |
| eqt(tag, tuplenil(H2)) | → | F | | eqt(true, nil) | → | F |
| eqt(true, a) | → | F | | eqt(true, excl) | → | F |
| eqt(true, false) | → | F | | eqt(true, lock) | → | F |
| eqt(true, locker) | → | F | | eqt(true, mcrlrecord) | → | F |
| eqt(true, ok) | → | F | | eqt(true, pending) | → | F |
| eqt(true, release) | → | F | | eqt(true, request) | → | F |
| eqt(true, resource) | → | F | | eqt(true, tag) | → | F |
| eqt(true, true) | → | T | | eqt(true, undefined) | → | F |
| eqt(true, pid(N2)) | → | F | | eqt(true, int(N2)) | → | F |
| eqt(true, cons(H2, T2)) | → | F | | eqt(true, tuple(H2, T2)) | → | F |
| eqt(true, tuplenil(H2)) | → | F | | eqt(undefined, nil) | → | F |
| eqt(undefined, a) | → | F | | eqt(undefined, tuplenil(H2)) | → | F |
| eqt(pid(N1), nil) | → | F | | eqt(pid(N1), a) | → | F |
| eqt(pid(N1), excl) | → | F | | eqt(pid(N1), false) | → | F |
| eqt(pid(N1), lock) | → | F | | eqt(pid(N1), locker) | → | F |
| eqt(pid(N1), mcrlrecord) | → | F | | eqt(pid(N1), ok) | → | F |
| eqt(pid(N1), pending) | → | F | | eqt(pid(N1), release) | → | F |
| eqt(pid(N1), request) | → | F | | eqt(pid(N1), resource) | → | F |
| eqt(pid(N1), tag) | → | F | | eqt(pid(N1), true) | → | F |
| eqt(pid(N1), undefined) | → | F | | eqt(pid(N1), pid(N2)) | → | eqt(N1, N2) |
| eqt(pid(N1), int(N2)) | → | F | | eqt(pid(N1), cons(H2, T2)) | → | F |
| eqt(pid(N1), tuple(H2, T2)) | → | F | | eqt(pid(N1), tuplenil(H2)) | → | F |
| eqt(int(N1), nil) | → | F | | eqt(int(N1), a) | → | F |
| eqt(int(N1), excl) | → | F | | eqt(int(N1), false) | → | F |
| eqt(int(N1), lock) | → | F | | eqt(int(N1), locker) | → | F |
| eqt(int(N1), mcrlrecord) | → | F | | eqt(int(N1), ok) | → | F |
| eqt(int(N1), pending) | → | F | | eqt(int(N1), release) | → | F |
| eqt(int(N1), request) | → | F | | eqt(int(N1), resource) | → | F |
| eqt(int(N1), tag) | → | F | | eqt(int(N1), true) | → | F |
| eqt(int(N1), undefined) | → | F | | eqt(cons(H1, T1), resource) | → | F |
| eqt(cons(H1, T1), tag) | → | F | | eqt(cons(H1, T1), true) | → | F |
| eqt(cons(H1, T1), undefined) | → | F | | eqt(cons(H1, T1), pid(N2)) | → | F |
| eqt(cons(H1, T1), int(N2)) | → | F | | eqt(cons(H1, T1), cons(H2, T2)) | → | and(eqt(H1, H2), eqt(T1, T2)) |
| eqt(cons(H1, T1), tuple(H2, T2)) | → | F | | eqt(cons(H1, T1), tuplenil(H2)) | → | F |
| eqt(tuple(H1, T1), nil) | → | F | | eqt(tuple(H1, T1), a) | → | F |
| eqt(tuple(H1, T1), excl) | → | F | | eqt(tuple(H1, T1), false) | → | F |
| eqt(tuple(H1, T1), lock) | → | F | | eqt(tuple(H1, T1), locker) | → | F |
| eqt(tuple(H1, T1), mcrlrecord) | → | F | | eqt(tuple(H1, T1), ok) | → | F |
| eqt(tuple(H1, T1), pending) | → | F | | eqt(tuple(H1, T1), release) | → | F |
| eqt(tuple(H1, T1), request) | → | F | | eqt(tuple(H1, T1), resource) | → | F |
| eqt(tuple(H1, T1), tag) | → | F | | eqt(tuple(H1, T1), true) | → | F |
| eqt(tuple(H1, T1), undefined) | → | F | | eqt(tuple(H1, T1), pid(N2)) | → | F |
| eqt(tuple(H1, T1), int(N2)) | → | F | | eqt(tuple(H1, T1), cons(H2, T2)) | → | F |
| eqt(tuple(H1, T1), tuple(H2, T2)) | → | and(eqt(H1, H2), eqt(T1, T2)) | | eqt(tuple(H1, T1), tuplenil(H2)) | → | F |
| eqt(tuplenil(H1), nil) | → | F | | eqt(tuplenil(H1), a) | → | F |
| eqt(tuplenil(H1), excl) | → | F | | eqt(tuplenil(H1), false) | → | F |
| eqt(tuplenil(H1), lock) | → | F | | eqt(tuplenil(H1), locker) | → | F |
| eqt(tuplenil(H1), mcrlrecord) | → | F | | eqt(tuplenil(H1), ok) | → | F |
| eqt(tuplenil(H1), pending) | → | F | | eqt(tuplenil(H1), release) | → | F |
| eqt(tuplenil(H1), request) | → | F | | eqt(tuplenil(H1), resource) | → | F |
| eqt(tuplenil(H1), tag) | → | F | | eqt(tuplenil(H1), true) | → | F |
| eqt(tuplenil(H1), undefined) | → | F | | eqt(tuplenil(H1), pid(N2)) | → | F |
| eqt(tuplenil(H1), int(N2)) | → | F | | eqt(tuplenil(H1), cons(H2, T2)) | → | F |
| eqt(tuplenil(H1), tuple(H2, T2)) | → | F | | eqt(tuplenil(H1), tuplenil(H2)) | → | eqt(H1, H2) |
| element(int(s(0)), tuplenil(T1)) | → | T1 | | element(int(s(0)), tuple(T1, T2)) | → | T1 |
| element(int(s(s(N1))), tuple(T1, T2)) | → | element(int(s(N1)), T2) | | record_new(lock) | → | tuple(mcrlrecord, tuple(lock, tuple(undefined, tuple(nil, tuplenil(nil))))) |
| record_extract(tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2))))), lock, resource) | → | tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2))))) | | record_update(tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2))))), lock, pending, NewF) | → | tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(NewF))))) |
| record_updates(Record, Name, nil) | → | Record | | record_updates(Record, Name, cons(tuple(Field, tuplenil(NewF)), Fields)) | → | record_updates(record_update(Record, Name, Field, NewF), Name, Fields) |
| locker2_map_promote_pending(nil, Pending) | → | nil | | locker2_map_promote_pending(cons(Lock, Locks), Pending) | → | cons(locker2_promote_pending(Lock, Pending), locker2_map_promote_pending(Locks, Pending)) |
| locker2_map_claim_lock(nil, Resources, Client) | → | nil | | locker2_map_claim_lock(cons(Lock, Locks), Resources, Client) | → | cons(locker2_claim_lock(Lock, Resources, Client), locker2_map_claim_lock(Locks, Resources, Client)) |
| locker2_map_add_pending(nil, Resources, Client) | → | nil | | locker2_promote_pending(Lock, Client) | → | case0(Client, Lock, record_extract(Lock, lock, pending)) |
| case0(Client, Lock, cons(Client, Pendings)) | → | record_updates(Lock, lock, cons(tuple(excl, tuplenil(Client)), cons(tuple(pending, tuplenil(Pendings)), nil))) | | case0(Client, Lock, MCRLFree0) | → | Lock |
| locker2_remove_pending(Lock, Client) | → | record_updates(Lock, lock, cons(tuple(pending, tuplenil(subtract(record_extract(Lock, lock, pending), cons(Client, nil)))), nil)) | | locker2_add_pending(Lock, Resources, Client) | → | case1(Client, Resources, Lock, member(record_extract(Lock, lock, resource), Resources)) |
| case1(Client, Resources, Lock, true) | → | record_updates(Lock, lock, cons(tuple(pending, tuplenil(append(record_extract(Lock, lock, pending), cons(Client, nil)))), nil)) | | case1(Client, Resources, Lock, false) | → | Lock |
| locker2_release_lock(Lock, Client) | → | case2(Client, Lock, gen_modtageq(Client, record_extract(Lock, lock, excl))) | | case2(Client, Lock, true) | → | record_updates(Lock, lock, cons(tuple(excllock, excl), nil)) |
| case4(Client, Lock, MCRLFree1) | → | false | | locker2_obtainables(nil, Client) | → | true |
| locker2_obtainables(cons(Lock, Locks), Client) | → | case5(Client, Locks, Lock, member(Client, record_extract(Lock, lock, pending))) | | case5(Client, Locks, Lock, true) | → | andt(locker2_obtainable(Lock, Client), locker2_obtainables(Locks, Client)) |
| case5(Client, Locks, Lock, false) | → | locker2_obtainables(Locks, Client) | | locker2_check_available(Resource, nil) | → | false |
| locker2_check_available(Resource, cons(Lock, Locks)) | → | case6(Locks, Lock, Resource, equal(Resource, record_extract(Lock, lock, resource))) | | case6(Locks, Lock, Resource, true) | → | andt(equal(record_extract(Lock, lock, excl), nil), equal(record_extract(Lock, lock, pending), nil)) |
| case6(Locks, Lock, Resource, false) | → | locker2_check_available(Resource, Locks) | | locker2_check_availables(nil, Locks) | → | true |
| locker2_check_availables(cons(Resource, Resources), Locks) | → | andt(locker2_check_available(Resource, Locks), locker2_check_availables(Resources, Locks)) | | locker2_adduniq(nil, List) | → | List |
| append(cons(Head, Tail), List) | → | cons(Head, append(Tail, List)) | | subtract(List, nil) | → | List |
| subtract(List, cons(Head, Tail)) | → | subtract(delete(Head, List), Tail) | | delete(E, nil) | → | nil |
| delete(E, cons(Head, Tail)) | → | case8(Tail, Head, E, equal(E, Head)) | | case8(Tail, Head, E, true) | → | Tail |
| case8(Tail, Head, E, false) | → | cons(Head, delete(E, Tail)) | | gen_tag(Pid) | → | tuple(Pid, tuplenil(tag)) |
| gen_modtageq(Client1, Client2) | → | equal(Client1, Client2) | | member(E, nil) | → | false |
| member(E, cons(Head, Tail)) | → | case9(Tail, Head, E, equal(E, Head)) | | case9(Tail, Head, E, true) | → | true |
| case9(Tail, Head, E, false) | → | member(E, Tail) | | eqs(empty, empty) | → | T |
| eqs(empty, stack(E2, S2)) | → | F | | eqs(stack(E1, S1), empty) | → | F |
| eqs(stack(E1, S1), stack(E2, S2)) | → | and(eqt(E1, E2), eqs(S1, S2)) | | pushs(E1, S1) | → | stack(E1, S1) |
| pops(stack(E1, S1)) | → | S1 | | tops(stack(E1, S1)) | → | E1 |
| istops(E1, empty) | → | F | | istops(E1, stack(E2, S1)) | → | eqt(E1, E2) |
| eqc(nocalls, nocalls) | → | T | | eqc(nocalls, calls(E2, S2, CS2)) | → | F |
| eqc(calls(E1, S1, CS1), nocalls) | → | F | | eqc(calls(E1, S1, CS1), calls(E2, S2, CS2)) | → | and(eqt(E1, E2), and(eqs(S1, S2), eqc(CS1, CS2))) |
| push(E1, E2, nocalls) | → | calls(E1, stack(E2, empty), nocalls) | | push(E1, E2, calls(E3, S1, CS1)) | → | push1(E1, E2, E3, S1, CS1, eqt(E1, E3)) |
| push1(E1, E2, E3, S1, CS1, T) | → | calls(E3, pushs(E2, S1), CS1) |
Original Signature
Termination of terms over the following signature is verified: tuplenil, record_new, tuple, tag, gen_tag, imp, locker2_map_promote_pending, pops, locker2_check_availables, mcrlrecord, pending, request, empty, false, ok, istops, locker2_add_pending, andt, case2, append, element, case1, case0, tops, push1, case6, case5, or, int, case4, record_extract, locker, case9, case8, locker2_map_add_pending, calls, eqc, and, not, 0, locker2_promote_pending, locker2_claim_lock, locker2_adduniq, stack, release, locker2_obtainables, F, locker2_remove_pending, push, T, gen_modtageq, record_update, undefined, if, record_updates, eqt, excllock, delete, eqs, cons, member, locker2_map_claim_lock, locker2_obtainable, a, pushs, resource, lock, true, locker2_release_lock, pid, equal, subtract, locker2_check_available, s, excl, nil, eq, nocalls
Strategy
Projection
The following projection was used:
- π (locker2_obtainables#): 1
- π (case5#): 2
Thus, the following dependency pairs are removed:
| locker2_obtainables#(cons(Lock, Locks), Client) | → | case5#(Client, Locks, Lock, member(Client, record_extract(Lock, lock, pending))) |
Problem 13: DependencyGraph
Dependency Pair Problem
Dependency Pairs
| case5#(Client, Locks, Lock, true) | → | locker2_obtainables#(Locks, Client) | | case5#(Client, Locks, Lock, false) | → | locker2_obtainables#(Locks, Client) |
Rewrite Rules
| or(T, T) | → | T | | or(F, T) | → | T |
| or(T, F) | → | T | | or(F, F) | → | F |
| and(T, B) | → | B | | and(B, T) | → | B |
| and(F, B) | → | F | | and(B, F) | → | F |
| imp(T, B) | → | B | | imp(F, B) | → | T |
| not(T) | → | F | | not(F) | → | T |
| if(T, B1, B2) | → | B1 | | if(F, B1, B2) | → | B2 |
| eq(T, T) | → | T | | eq(F, F) | → | T |
| eq(T, F) | → | F | | eq(F, T) | → | F |
| eqt(nil, undefined) | → | F | | eqt(nil, pid(N2)) | → | F |
| eqt(nil, int(N2)) | → | F | | eqt(nil, cons(H2, T2)) | → | F |
| eqt(nil, tuple(H2, T2)) | → | F | | eqt(nil, tuplenil(H2)) | → | F |
| eqt(a, nil) | → | F | | eqt(a, a) | → | T |
| eqt(a, excl) | → | F | | eqt(a, false) | → | F |
| eqt(a, lock) | → | F | | eqt(a, locker) | → | F |
| eqt(a, mcrlrecord) | → | F | | eqt(a, ok) | → | F |
| eqt(a, pending) | → | F | | eqt(a, release) | → | F |
| eqt(a, request) | → | F | | eqt(a, resource) | → | F |
| eqt(a, tag) | → | F | | eqt(a, true) | → | F |
| eqt(a, undefined) | → | F | | eqt(a, pid(N2)) | → | F |
| eqt(a, int(N2)) | → | F | | eqt(a, cons(H2, T2)) | → | F |
| eqt(a, tuple(H2, T2)) | → | F | | eqt(a, tuplenil(H2)) | → | F |
| eqt(excl, nil) | → | F | | eqt(excl, a) | → | F |
| eqt(excl, excl) | → | T | | eqt(excl, false) | → | F |
| eqt(excl, lock) | → | F | | eqt(excl, locker) | → | F |
| eqt(excl, mcrlrecord) | → | F | | eqt(excl, ok) | → | F |
| eqt(excl, pending) | → | F | | eqt(excl, release) | → | F |
| eqt(excl, request) | → | F | | eqt(excl, resource) | → | F |
| eqt(excl, tag) | → | F | | eqt(excl, true) | → | F |
| eqt(excl, undefined) | → | F | | eqt(excl, pid(N2)) | → | F |
| eqt(excl, eqt(false, int(N2))) | → | F | | eqt(false, cons(H2, T2)) | → | F |
| eqt(false, tuple(H2, T2)) | → | F | | eqt(false, tuplenil(H2)) | → | F |
| eqt(lock, nil) | → | F | | eqt(lock, a) | → | F |
| eqt(lock, excl) | → | F | | eqt(lock, false) | → | F |
| eqt(lock, lock) | → | T | | eqt(lock, locker) | → | F |
| eqt(lock, mcrlrecord) | → | F | | eqt(lock, ok) | → | F |
| eqt(lock, pending) | → | F | | eqt(lock, release) | → | F |
| eqt(lock, request) | → | F | | eqt(lock, resource) | → | F |
| eqt(lock, tag) | → | F | | eqt(lock, true) | → | F |
| eqt(lock, undefined) | → | F | | eqt(lock, pid(N2)) | → | F |
| eqt(lock, int(N2)) | → | F | | eqt(lock, cons(H2, T2)) | → | F |
| eqt(lock, tuple(H2, T2)) | → | F | | eqt(lock, tuplenil(H2)) | → | F |
| eqt(locker, nil) | → | F | | eqt(locker, a) | → | F |
| eqt(locker, excl) | → | F | | eqt(locker, false) | → | F |
| eqt(locker, lock) | → | F | | eqt(locker, locker) | → | T |
| eqt(locker, mcrlrecord) | → | F | | eqt(locker, ok) | → | F |
| eqt(locker, pending) | → | F | | eqt(locker, release) | → | F |
| eqt(locker, request) | → | F | | eqt(locker, resource) | → | F |
| eqt(locker, tag) | → | F | | eqt(locker, true) | → | F |
| eqt(locker, undefined) | → | F | | eqt(locker, pid(N2)) | → | F |
| eqt(locker, int(N2)) | → | F | | eqt(locker, cons(H2, T2)) | → | F |
| eqt(locker, tuple(H2, T2)) | → | F | | eqt(locker, tuplenil(H2)) | → | F |
| eqt(mcrlrecord, nil) | → | F | | eqt(mcrlrecord, a) | → | F |
| eqt(mcrlrecord, excl) | → | F | | eqt(mcrlrecord, false) | → | F |
| eqt(mcrlrecord, lock) | → | F | | eqt(mcrlrecord, locker) | → | F |
| eqt(mcrlrecord, mcrlrecord) | → | T | | eqt(mcrlrecord, ok) | → | F |
| eqt(mcrlrecord, pending) | → | F | | eqt(mcrlrecord, release) | → | F |
| eqt(mcrlrecord, request) | → | F | | eqt(mcrlrecord, resource) | → | F |
| eqt(ok, resource) | → | F | | eqt(ok, tag) | → | F |
| eqt(ok, true) | → | F | | eqt(ok, undefined) | → | F |
| eqt(ok, pid(N2)) | → | F | | eqt(ok, int(N2)) | → | F |
| eqt(ok, cons(H2, T2)) | → | F | | eqt(ok, tuple(H2, T2)) | → | F |
| eqt(ok, tuplenil(H2)) | → | F | | eqt(pending, nil) | → | F |
| eqt(pending, a) | → | F | | eqt(pending, excl) | → | F |
| eqt(pending, false) | → | F | | eqt(pending, lock) | → | F |
| eqt(pending, locker) | → | F | | eqt(pending, mcrlrecord) | → | F |
| eqt(pending, ok) | → | F | | eqt(pending, pending) | → | T |
| eqt(pending, release) | → | F | | eqt(pending, request) | → | F |
| eqt(pending, resource) | → | F | | eqt(pending, tag) | → | F |
| eqt(pending, true) | → | F | | eqt(pending, undefined) | → | F |
| eqt(pending, pid(N2)) | → | F | | eqt(pending, int(N2)) | → | F |
| eqt(pending, cons(H2, T2)) | → | F | | eqt(pending, tuple(H2, T2)) | → | F |
| eqt(pending, tuplenil(H2)) | → | F | | eqt(release, nil) | → | F |
| eqt(release, a) | → | F | | eqt(release, excl) | → | F |
| eqt(release, false) | → | F | | eqt(release, lock) | → | F |
| eqt(release, locker) | → | F | | eqt(release, mcrlrecord) | → | F |
| eqt(release, ok) | → | F | | eqt(request, mcrlrecord) | → | F |
| eqt(request, ok) | → | F | | eqt(request, pending) | → | F |
| eqt(request, release) | → | F | | eqt(request, request) | → | T |
| eqt(request, resource) | → | F | | eqt(request, tag) | → | F |
| eqt(request, true) | → | F | | eqt(request, undefined) | → | F |
| eqt(request, pid(N2)) | → | F | | eqt(request, int(N2)) | → | F |
| eqt(request, cons(H2, T2)) | → | F | | eqt(request, tuple(H2, T2)) | → | F |
| eqt(request, tuplenil(H2)) | → | F | | eqt(resource, nil) | → | F |
| eqt(resource, a) | → | F | | eqt(resource, excl) | → | F |
| eqt(resource, false) | → | F | | eqt(resource, lock) | → | F |
| eqt(resource, locker) | → | F | | eqt(resource, mcrlrecord) | → | F |
| eqt(resource, ok) | → | F | | eqt(resource, pending) | → | F |
| eqt(resource, release) | → | F | | eqt(resource, request) | → | F |
| eqt(resource, resource) | → | T | | eqt(resource, tag) | → | F |
| eqt(resource, true) | → | F | | eqt(resource, undefined) | → | F |
| eqt(resource, pid(N2)) | → | F | | eqt(resource, int(N2)) | → | F |
| eqt(resource, cons(H2, T2)) | → | F | | eqt(resource, tuple(H2, T2)) | → | F |
| eqt(resource, tuplenil(H2)) | → | F | | eqt(tag, nil) | → | F |
| eqt(tag, a) | → | F | | eqt(tag, excl) | → | F |
| eqt(tag, false) | → | F | | eqt(tag, lock) | → | F |
| eqt(tag, locker) | → | F | | eqt(tag, mcrlrecord) | → | F |
| eqt(tag, ok) | → | F | | eqt(tag, pending) | → | F |
| eqt(tag, release) | → | F | | eqt(tag, request) | → | F |
| eqt(tag, resource) | → | F | | eqt(tag, tag) | → | T |
| eqt(tag, true) | → | F | | eqt(tag, undefined) | → | F |
| eqt(tag, pid(N2)) | → | F | | eqt(tag, int(N2)) | → | F |
| eqt(tag, cons(H2, T2)) | → | F | | eqt(tag, tuple(H2, T2)) | → | F |
| eqt(tag, tuplenil(H2)) | → | F | | eqt(true, nil) | → | F |
| eqt(true, a) | → | F | | eqt(true, excl) | → | F |
| eqt(true, false) | → | F | | eqt(true, lock) | → | F |
| eqt(true, locker) | → | F | | eqt(true, mcrlrecord) | → | F |
| eqt(true, ok) | → | F | | eqt(true, pending) | → | F |
| eqt(true, release) | → | F | | eqt(true, request) | → | F |
| eqt(true, resource) | → | F | | eqt(true, tag) | → | F |
| eqt(true, true) | → | T | | eqt(true, undefined) | → | F |
| eqt(true, pid(N2)) | → | F | | eqt(true, int(N2)) | → | F |
| eqt(true, cons(H2, T2)) | → | F | | eqt(true, tuple(H2, T2)) | → | F |
| eqt(true, tuplenil(H2)) | → | F | | eqt(undefined, nil) | → | F |
| eqt(undefined, a) | → | F | | eqt(undefined, tuplenil(H2)) | → | F |
| eqt(pid(N1), nil) | → | F | | eqt(pid(N1), a) | → | F |
| eqt(pid(N1), excl) | → | F | | eqt(pid(N1), false) | → | F |
| eqt(pid(N1), lock) | → | F | | eqt(pid(N1), locker) | → | F |
| eqt(pid(N1), mcrlrecord) | → | F | | eqt(pid(N1), ok) | → | F |
| eqt(pid(N1), pending) | → | F | | eqt(pid(N1), release) | → | F |
| eqt(pid(N1), request) | → | F | | eqt(pid(N1), resource) | → | F |
| eqt(pid(N1), tag) | → | F | | eqt(pid(N1), true) | → | F |
| eqt(pid(N1), undefined) | → | F | | eqt(pid(N1), pid(N2)) | → | eqt(N1, N2) |
| eqt(pid(N1), int(N2)) | → | F | | eqt(pid(N1), cons(H2, T2)) | → | F |
| eqt(pid(N1), tuple(H2, T2)) | → | F | | eqt(pid(N1), tuplenil(H2)) | → | F |
| eqt(int(N1), nil) | → | F | | eqt(int(N1), a) | → | F |
| eqt(int(N1), excl) | → | F | | eqt(int(N1), false) | → | F |
| eqt(int(N1), lock) | → | F | | eqt(int(N1), locker) | → | F |
| eqt(int(N1), mcrlrecord) | → | F | | eqt(int(N1), ok) | → | F |
| eqt(int(N1), pending) | → | F | | eqt(int(N1), release) | → | F |
| eqt(int(N1), request) | → | F | | eqt(int(N1), resource) | → | F |
| eqt(int(N1), tag) | → | F | | eqt(int(N1), true) | → | F |
| eqt(int(N1), undefined) | → | F | | eqt(cons(H1, T1), resource) | → | F |
| eqt(cons(H1, T1), tag) | → | F | | eqt(cons(H1, T1), true) | → | F |
| eqt(cons(H1, T1), undefined) | → | F | | eqt(cons(H1, T1), pid(N2)) | → | F |
| eqt(cons(H1, T1), int(N2)) | → | F | | eqt(cons(H1, T1), cons(H2, T2)) | → | and(eqt(H1, H2), eqt(T1, T2)) |
| eqt(cons(H1, T1), tuple(H2, T2)) | → | F | | eqt(cons(H1, T1), tuplenil(H2)) | → | F |
| eqt(tuple(H1, T1), nil) | → | F | | eqt(tuple(H1, T1), a) | → | F |
| eqt(tuple(H1, T1), excl) | → | F | | eqt(tuple(H1, T1), false) | → | F |
| eqt(tuple(H1, T1), lock) | → | F | | eqt(tuple(H1, T1), locker) | → | F |
| eqt(tuple(H1, T1), mcrlrecord) | → | F | | eqt(tuple(H1, T1), ok) | → | F |
| eqt(tuple(H1, T1), pending) | → | F | | eqt(tuple(H1, T1), release) | → | F |
| eqt(tuple(H1, T1), request) | → | F | | eqt(tuple(H1, T1), resource) | → | F |
| eqt(tuple(H1, T1), tag) | → | F | | eqt(tuple(H1, T1), true) | → | F |
| eqt(tuple(H1, T1), undefined) | → | F | | eqt(tuple(H1, T1), pid(N2)) | → | F |
| eqt(tuple(H1, T1), int(N2)) | → | F | | eqt(tuple(H1, T1), cons(H2, T2)) | → | F |
| eqt(tuple(H1, T1), tuple(H2, T2)) | → | and(eqt(H1, H2), eqt(T1, T2)) | | eqt(tuple(H1, T1), tuplenil(H2)) | → | F |
| eqt(tuplenil(H1), nil) | → | F | | eqt(tuplenil(H1), a) | → | F |
| eqt(tuplenil(H1), excl) | → | F | | eqt(tuplenil(H1), false) | → | F |
| eqt(tuplenil(H1), lock) | → | F | | eqt(tuplenil(H1), locker) | → | F |
| eqt(tuplenil(H1), mcrlrecord) | → | F | | eqt(tuplenil(H1), ok) | → | F |
| eqt(tuplenil(H1), pending) | → | F | | eqt(tuplenil(H1), release) | → | F |
| eqt(tuplenil(H1), request) | → | F | | eqt(tuplenil(H1), resource) | → | F |
| eqt(tuplenil(H1), tag) | → | F | | eqt(tuplenil(H1), true) | → | F |
| eqt(tuplenil(H1), undefined) | → | F | | eqt(tuplenil(H1), pid(N2)) | → | F |
| eqt(tuplenil(H1), int(N2)) | → | F | | eqt(tuplenil(H1), cons(H2, T2)) | → | F |
| eqt(tuplenil(H1), tuple(H2, T2)) | → | F | | eqt(tuplenil(H1), tuplenil(H2)) | → | eqt(H1, H2) |
| element(int(s(0)), tuplenil(T1)) | → | T1 | | element(int(s(0)), tuple(T1, T2)) | → | T1 |
| element(int(s(s(N1))), tuple(T1, T2)) | → | element(int(s(N1)), T2) | | record_new(lock) | → | tuple(mcrlrecord, tuple(lock, tuple(undefined, tuple(nil, tuplenil(nil))))) |
| record_extract(tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2))))), lock, resource) | → | tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2))))) | | record_update(tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2))))), lock, pending, NewF) | → | tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(NewF))))) |
| record_updates(Record, Name, nil) | → | Record | | record_updates(Record, Name, cons(tuple(Field, tuplenil(NewF)), Fields)) | → | record_updates(record_update(Record, Name, Field, NewF), Name, Fields) |
| locker2_map_promote_pending(nil, Pending) | → | nil | | locker2_map_promote_pending(cons(Lock, Locks), Pending) | → | cons(locker2_promote_pending(Lock, Pending), locker2_map_promote_pending(Locks, Pending)) |
| locker2_map_claim_lock(nil, Resources, Client) | → | nil | | locker2_map_claim_lock(cons(Lock, Locks), Resources, Client) | → | cons(locker2_claim_lock(Lock, Resources, Client), locker2_map_claim_lock(Locks, Resources, Client)) |
| locker2_map_add_pending(nil, Resources, Client) | → | nil | | locker2_promote_pending(Lock, Client) | → | case0(Client, Lock, record_extract(Lock, lock, pending)) |
| case0(Client, Lock, cons(Client, Pendings)) | → | record_updates(Lock, lock, cons(tuple(excl, tuplenil(Client)), cons(tuple(pending, tuplenil(Pendings)), nil))) | | case0(Client, Lock, MCRLFree0) | → | Lock |
| locker2_remove_pending(Lock, Client) | → | record_updates(Lock, lock, cons(tuple(pending, tuplenil(subtract(record_extract(Lock, lock, pending), cons(Client, nil)))), nil)) | | locker2_add_pending(Lock, Resources, Client) | → | case1(Client, Resources, Lock, member(record_extract(Lock, lock, resource), Resources)) |
| case1(Client, Resources, Lock, true) | → | record_updates(Lock, lock, cons(tuple(pending, tuplenil(append(record_extract(Lock, lock, pending), cons(Client, nil)))), nil)) | | case1(Client, Resources, Lock, false) | → | Lock |
| locker2_release_lock(Lock, Client) | → | case2(Client, Lock, gen_modtageq(Client, record_extract(Lock, lock, excl))) | | case2(Client, Lock, true) | → | record_updates(Lock, lock, cons(tuple(excllock, excl), nil)) |
| case4(Client, Lock, MCRLFree1) | → | false | | locker2_obtainables(nil, Client) | → | true |
| locker2_obtainables(cons(Lock, Locks), Client) | → | case5(Client, Locks, Lock, member(Client, record_extract(Lock, lock, pending))) | | case5(Client, Locks, Lock, true) | → | andt(locker2_obtainable(Lock, Client), locker2_obtainables(Locks, Client)) |
| case5(Client, Locks, Lock, false) | → | locker2_obtainables(Locks, Client) | | locker2_check_available(Resource, nil) | → | false |
| locker2_check_available(Resource, cons(Lock, Locks)) | → | case6(Locks, Lock, Resource, equal(Resource, record_extract(Lock, lock, resource))) | | case6(Locks, Lock, Resource, true) | → | andt(equal(record_extract(Lock, lock, excl), nil), equal(record_extract(Lock, lock, pending), nil)) |
| case6(Locks, Lock, Resource, false) | → | locker2_check_available(Resource, Locks) | | locker2_check_availables(nil, Locks) | → | true |
| locker2_check_availables(cons(Resource, Resources), Locks) | → | andt(locker2_check_available(Resource, Locks), locker2_check_availables(Resources, Locks)) | | locker2_adduniq(nil, List) | → | List |
| append(cons(Head, Tail), List) | → | cons(Head, append(Tail, List)) | | subtract(List, nil) | → | List |
| subtract(List, cons(Head, Tail)) | → | subtract(delete(Head, List), Tail) | | delete(E, nil) | → | nil |
| delete(E, cons(Head, Tail)) | → | case8(Tail, Head, E, equal(E, Head)) | | case8(Tail, Head, E, true) | → | Tail |
| case8(Tail, Head, E, false) | → | cons(Head, delete(E, Tail)) | | gen_tag(Pid) | → | tuple(Pid, tuplenil(tag)) |
| gen_modtageq(Client1, Client2) | → | equal(Client1, Client2) | | member(E, nil) | → | false |
| member(E, cons(Head, Tail)) | → | case9(Tail, Head, E, equal(E, Head)) | | case9(Tail, Head, E, true) | → | true |
| case9(Tail, Head, E, false) | → | member(E, Tail) | | eqs(empty, empty) | → | T |
| eqs(empty, stack(E2, S2)) | → | F | | eqs(stack(E1, S1), empty) | → | F |
| eqs(stack(E1, S1), stack(E2, S2)) | → | and(eqt(E1, E2), eqs(S1, S2)) | | pushs(E1, S1) | → | stack(E1, S1) |
| pops(stack(E1, S1)) | → | S1 | | tops(stack(E1, S1)) | → | E1 |
| istops(E1, empty) | → | F | | istops(E1, stack(E2, S1)) | → | eqt(E1, E2) |
| eqc(nocalls, nocalls) | → | T | | eqc(nocalls, calls(E2, S2, CS2)) | → | F |
| eqc(calls(E1, S1, CS1), nocalls) | → | F | | eqc(calls(E1, S1, CS1), calls(E2, S2, CS2)) | → | and(eqt(E1, E2), and(eqs(S1, S2), eqc(CS1, CS2))) |
| push(E1, E2, nocalls) | → | calls(E1, stack(E2, empty), nocalls) | | push(E1, E2, calls(E3, S1, CS1)) | → | push1(E1, E2, E3, S1, CS1, eqt(E1, E3)) |
| push1(E1, E2, E3, S1, CS1, T) | → | calls(E3, pushs(E2, S1), CS1) |
Original Signature
Termination of terms over the following signature is verified: tuplenil, record_new, tuple, tag, gen_tag, imp, locker2_map_promote_pending, pops, locker2_check_availables, mcrlrecord, pending, request, empty, false, ok, istops, locker2_add_pending, andt, element, append, case2, case1, tops, case0, push1, case6, case5, or, int, case4, record_extract, locker, case9, case8, locker2_map_add_pending, calls, eqc, and, not, 0, locker2_promote_pending, locker2_claim_lock, locker2_adduniq, stack, release, locker2_obtainables, F, locker2_remove_pending, push, T, gen_modtageq, record_update, if, undefined, excllock, eqt, record_updates, eqs, delete, cons, member, locker2_map_claim_lock, locker2_obtainable, pushs, a, lock, resource, locker2_release_lock, true, equal, pid, subtract, locker2_check_available, s, excl, nocalls, eq, nil
Strategy
There are no SCCs!
Problem 7: SubtermCriterion
Dependency Pair Problem
Dependency Pairs
| eqc#(calls(E1, S1, CS1), calls(E2, S2, CS2)) | → | eqc#(CS1, CS2) |
Rewrite Rules
| or(T, T) | → | T | | or(F, T) | → | T |
| or(T, F) | → | T | | or(F, F) | → | F |
| and(T, B) | → | B | | and(B, T) | → | B |
| and(F, B) | → | F | | and(B, F) | → | F |
| imp(T, B) | → | B | | imp(F, B) | → | T |
| not(T) | → | F | | not(F) | → | T |
| if(T, B1, B2) | → | B1 | | if(F, B1, B2) | → | B2 |
| eq(T, T) | → | T | | eq(F, F) | → | T |
| eq(T, F) | → | F | | eq(F, T) | → | F |
| eqt(nil, undefined) | → | F | | eqt(nil, pid(N2)) | → | F |
| eqt(nil, int(N2)) | → | F | | eqt(nil, cons(H2, T2)) | → | F |
| eqt(nil, tuple(H2, T2)) | → | F | | eqt(nil, tuplenil(H2)) | → | F |
| eqt(a, nil) | → | F | | eqt(a, a) | → | T |
| eqt(a, excl) | → | F | | eqt(a, false) | → | F |
| eqt(a, lock) | → | F | | eqt(a, locker) | → | F |
| eqt(a, mcrlrecord) | → | F | | eqt(a, ok) | → | F |
| eqt(a, pending) | → | F | | eqt(a, release) | → | F |
| eqt(a, request) | → | F | | eqt(a, resource) | → | F |
| eqt(a, tag) | → | F | | eqt(a, true) | → | F |
| eqt(a, undefined) | → | F | | eqt(a, pid(N2)) | → | F |
| eqt(a, int(N2)) | → | F | | eqt(a, cons(H2, T2)) | → | F |
| eqt(a, tuple(H2, T2)) | → | F | | eqt(a, tuplenil(H2)) | → | F |
| eqt(excl, nil) | → | F | | eqt(excl, a) | → | F |
| eqt(excl, excl) | → | T | | eqt(excl, false) | → | F |
| eqt(excl, lock) | → | F | | eqt(excl, locker) | → | F |
| eqt(excl, mcrlrecord) | → | F | | eqt(excl, ok) | → | F |
| eqt(excl, pending) | → | F | | eqt(excl, release) | → | F |
| eqt(excl, request) | → | F | | eqt(excl, resource) | → | F |
| eqt(excl, tag) | → | F | | eqt(excl, true) | → | F |
| eqt(excl, undefined) | → | F | | eqt(excl, pid(N2)) | → | F |
| eqt(excl, eqt(false, int(N2))) | → | F | | eqt(false, cons(H2, T2)) | → | F |
| eqt(false, tuple(H2, T2)) | → | F | | eqt(false, tuplenil(H2)) | → | F |
| eqt(lock, nil) | → | F | | eqt(lock, a) | → | F |
| eqt(lock, excl) | → | F | | eqt(lock, false) | → | F |
| eqt(lock, lock) | → | T | | eqt(lock, locker) | → | F |
| eqt(lock, mcrlrecord) | → | F | | eqt(lock, ok) | → | F |
| eqt(lock, pending) | → | F | | eqt(lock, release) | → | F |
| eqt(lock, request) | → | F | | eqt(lock, resource) | → | F |
| eqt(lock, tag) | → | F | | eqt(lock, true) | → | F |
| eqt(lock, undefined) | → | F | | eqt(lock, pid(N2)) | → | F |
| eqt(lock, int(N2)) | → | F | | eqt(lock, cons(H2, T2)) | → | F |
| eqt(lock, tuple(H2, T2)) | → | F | | eqt(lock, tuplenil(H2)) | → | F |
| eqt(locker, nil) | → | F | | eqt(locker, a) | → | F |
| eqt(locker, excl) | → | F | | eqt(locker, false) | → | F |
| eqt(locker, lock) | → | F | | eqt(locker, locker) | → | T |
| eqt(locker, mcrlrecord) | → | F | | eqt(locker, ok) | → | F |
| eqt(locker, pending) | → | F | | eqt(locker, release) | → | F |
| eqt(locker, request) | → | F | | eqt(locker, resource) | → | F |
| eqt(locker, tag) | → | F | | eqt(locker, true) | → | F |
| eqt(locker, undefined) | → | F | | eqt(locker, pid(N2)) | → | F |
| eqt(locker, int(N2)) | → | F | | eqt(locker, cons(H2, T2)) | → | F |
| eqt(locker, tuple(H2, T2)) | → | F | | eqt(locker, tuplenil(H2)) | → | F |
| eqt(mcrlrecord, nil) | → | F | | eqt(mcrlrecord, a) | → | F |
| eqt(mcrlrecord, excl) | → | F | | eqt(mcrlrecord, false) | → | F |
| eqt(mcrlrecord, lock) | → | F | | eqt(mcrlrecord, locker) | → | F |
| eqt(mcrlrecord, mcrlrecord) | → | T | | eqt(mcrlrecord, ok) | → | F |
| eqt(mcrlrecord, pending) | → | F | | eqt(mcrlrecord, release) | → | F |
| eqt(mcrlrecord, request) | → | F | | eqt(mcrlrecord, resource) | → | F |
| eqt(ok, resource) | → | F | | eqt(ok, tag) | → | F |
| eqt(ok, true) | → | F | | eqt(ok, undefined) | → | F |
| eqt(ok, pid(N2)) | → | F | | eqt(ok, int(N2)) | → | F |
| eqt(ok, cons(H2, T2)) | → | F | | eqt(ok, tuple(H2, T2)) | → | F |
| eqt(ok, tuplenil(H2)) | → | F | | eqt(pending, nil) | → | F |
| eqt(pending, a) | → | F | | eqt(pending, excl) | → | F |
| eqt(pending, false) | → | F | | eqt(pending, lock) | → | F |
| eqt(pending, locker) | → | F | | eqt(pending, mcrlrecord) | → | F |
| eqt(pending, ok) | → | F | | eqt(pending, pending) | → | T |
| eqt(pending, release) | → | F | | eqt(pending, request) | → | F |
| eqt(pending, resource) | → | F | | eqt(pending, tag) | → | F |
| eqt(pending, true) | → | F | | eqt(pending, undefined) | → | F |
| eqt(pending, pid(N2)) | → | F | | eqt(pending, int(N2)) | → | F |
| eqt(pending, cons(H2, T2)) | → | F | | eqt(pending, tuple(H2, T2)) | → | F |
| eqt(pending, tuplenil(H2)) | → | F | | eqt(release, nil) | → | F |
| eqt(release, a) | → | F | | eqt(release, excl) | → | F |
| eqt(release, false) | → | F | | eqt(release, lock) | → | F |
| eqt(release, locker) | → | F | | eqt(release, mcrlrecord) | → | F |
| eqt(release, ok) | → | F | | eqt(request, mcrlrecord) | → | F |
| eqt(request, ok) | → | F | | eqt(request, pending) | → | F |
| eqt(request, release) | → | F | | eqt(request, request) | → | T |
| eqt(request, resource) | → | F | | eqt(request, tag) | → | F |
| eqt(request, true) | → | F | | eqt(request, undefined) | → | F |
| eqt(request, pid(N2)) | → | F | | eqt(request, int(N2)) | → | F |
| eqt(request, cons(H2, T2)) | → | F | | eqt(request, tuple(H2, T2)) | → | F |
| eqt(request, tuplenil(H2)) | → | F | | eqt(resource, nil) | → | F |
| eqt(resource, a) | → | F | | eqt(resource, excl) | → | F |
| eqt(resource, false) | → | F | | eqt(resource, lock) | → | F |
| eqt(resource, locker) | → | F | | eqt(resource, mcrlrecord) | → | F |
| eqt(resource, ok) | → | F | | eqt(resource, pending) | → | F |
| eqt(resource, release) | → | F | | eqt(resource, request) | → | F |
| eqt(resource, resource) | → | T | | eqt(resource, tag) | → | F |
| eqt(resource, true) | → | F | | eqt(resource, undefined) | → | F |
| eqt(resource, pid(N2)) | → | F | | eqt(resource, int(N2)) | → | F |
| eqt(resource, cons(H2, T2)) | → | F | | eqt(resource, tuple(H2, T2)) | → | F |
| eqt(resource, tuplenil(H2)) | → | F | | eqt(tag, nil) | → | F |
| eqt(tag, a) | → | F | | eqt(tag, excl) | → | F |
| eqt(tag, false) | → | F | | eqt(tag, lock) | → | F |
| eqt(tag, locker) | → | F | | eqt(tag, mcrlrecord) | → | F |
| eqt(tag, ok) | → | F | | eqt(tag, pending) | → | F |
| eqt(tag, release) | → | F | | eqt(tag, request) | → | F |
| eqt(tag, resource) | → | F | | eqt(tag, tag) | → | T |
| eqt(tag, true) | → | F | | eqt(tag, undefined) | → | F |
| eqt(tag, pid(N2)) | → | F | | eqt(tag, int(N2)) | → | F |
| eqt(tag, cons(H2, T2)) | → | F | | eqt(tag, tuple(H2, T2)) | → | F |
| eqt(tag, tuplenil(H2)) | → | F | | eqt(true, nil) | → | F |
| eqt(true, a) | → | F | | eqt(true, excl) | → | F |
| eqt(true, false) | → | F | | eqt(true, lock) | → | F |
| eqt(true, locker) | → | F | | eqt(true, mcrlrecord) | → | F |
| eqt(true, ok) | → | F | | eqt(true, pending) | → | F |
| eqt(true, release) | → | F | | eqt(true, request) | → | F |
| eqt(true, resource) | → | F | | eqt(true, tag) | → | F |
| eqt(true, true) | → | T | | eqt(true, undefined) | → | F |
| eqt(true, pid(N2)) | → | F | | eqt(true, int(N2)) | → | F |
| eqt(true, cons(H2, T2)) | → | F | | eqt(true, tuple(H2, T2)) | → | F |
| eqt(true, tuplenil(H2)) | → | F | | eqt(undefined, nil) | → | F |
| eqt(undefined, a) | → | F | | eqt(undefined, tuplenil(H2)) | → | F |
| eqt(pid(N1), nil) | → | F | | eqt(pid(N1), a) | → | F |
| eqt(pid(N1), excl) | → | F | | eqt(pid(N1), false) | → | F |
| eqt(pid(N1), lock) | → | F | | eqt(pid(N1), locker) | → | F |
| eqt(pid(N1), mcrlrecord) | → | F | | eqt(pid(N1), ok) | → | F |
| eqt(pid(N1), pending) | → | F | | eqt(pid(N1), release) | → | F |
| eqt(pid(N1), request) | → | F | | eqt(pid(N1), resource) | → | F |
| eqt(pid(N1), tag) | → | F | | eqt(pid(N1), true) | → | F |
| eqt(pid(N1), undefined) | → | F | | eqt(pid(N1), pid(N2)) | → | eqt(N1, N2) |
| eqt(pid(N1), int(N2)) | → | F | | eqt(pid(N1), cons(H2, T2)) | → | F |
| eqt(pid(N1), tuple(H2, T2)) | → | F | | eqt(pid(N1), tuplenil(H2)) | → | F |
| eqt(int(N1), nil) | → | F | | eqt(int(N1), a) | → | F |
| eqt(int(N1), excl) | → | F | | eqt(int(N1), false) | → | F |
| eqt(int(N1), lock) | → | F | | eqt(int(N1), locker) | → | F |
| eqt(int(N1), mcrlrecord) | → | F | | eqt(int(N1), ok) | → | F |
| eqt(int(N1), pending) | → | F | | eqt(int(N1), release) | → | F |
| eqt(int(N1), request) | → | F | | eqt(int(N1), resource) | → | F |
| eqt(int(N1), tag) | → | F | | eqt(int(N1), true) | → | F |
| eqt(int(N1), undefined) | → | F | | eqt(cons(H1, T1), resource) | → | F |
| eqt(cons(H1, T1), tag) | → | F | | eqt(cons(H1, T1), true) | → | F |
| eqt(cons(H1, T1), undefined) | → | F | | eqt(cons(H1, T1), pid(N2)) | → | F |
| eqt(cons(H1, T1), int(N2)) | → | F | | eqt(cons(H1, T1), cons(H2, T2)) | → | and(eqt(H1, H2), eqt(T1, T2)) |
| eqt(cons(H1, T1), tuple(H2, T2)) | → | F | | eqt(cons(H1, T1), tuplenil(H2)) | → | F |
| eqt(tuple(H1, T1), nil) | → | F | | eqt(tuple(H1, T1), a) | → | F |
| eqt(tuple(H1, T1), excl) | → | F | | eqt(tuple(H1, T1), false) | → | F |
| eqt(tuple(H1, T1), lock) | → | F | | eqt(tuple(H1, T1), locker) | → | F |
| eqt(tuple(H1, T1), mcrlrecord) | → | F | | eqt(tuple(H1, T1), ok) | → | F |
| eqt(tuple(H1, T1), pending) | → | F | | eqt(tuple(H1, T1), release) | → | F |
| eqt(tuple(H1, T1), request) | → | F | | eqt(tuple(H1, T1), resource) | → | F |
| eqt(tuple(H1, T1), tag) | → | F | | eqt(tuple(H1, T1), true) | → | F |
| eqt(tuple(H1, T1), undefined) | → | F | | eqt(tuple(H1, T1), pid(N2)) | → | F |
| eqt(tuple(H1, T1), int(N2)) | → | F | | eqt(tuple(H1, T1), cons(H2, T2)) | → | F |
| eqt(tuple(H1, T1), tuple(H2, T2)) | → | and(eqt(H1, H2), eqt(T1, T2)) | | eqt(tuple(H1, T1), tuplenil(H2)) | → | F |
| eqt(tuplenil(H1), nil) | → | F | | eqt(tuplenil(H1), a) | → | F |
| eqt(tuplenil(H1), excl) | → | F | | eqt(tuplenil(H1), false) | → | F |
| eqt(tuplenil(H1), lock) | → | F | | eqt(tuplenil(H1), locker) | → | F |
| eqt(tuplenil(H1), mcrlrecord) | → | F | | eqt(tuplenil(H1), ok) | → | F |
| eqt(tuplenil(H1), pending) | → | F | | eqt(tuplenil(H1), release) | → | F |
| eqt(tuplenil(H1), request) | → | F | | eqt(tuplenil(H1), resource) | → | F |
| eqt(tuplenil(H1), tag) | → | F | | eqt(tuplenil(H1), true) | → | F |
| eqt(tuplenil(H1), undefined) | → | F | | eqt(tuplenil(H1), pid(N2)) | → | F |
| eqt(tuplenil(H1), int(N2)) | → | F | | eqt(tuplenil(H1), cons(H2, T2)) | → | F |
| eqt(tuplenil(H1), tuple(H2, T2)) | → | F | | eqt(tuplenil(H1), tuplenil(H2)) | → | eqt(H1, H2) |
| element(int(s(0)), tuplenil(T1)) | → | T1 | | element(int(s(0)), tuple(T1, T2)) | → | T1 |
| element(int(s(s(N1))), tuple(T1, T2)) | → | element(int(s(N1)), T2) | | record_new(lock) | → | tuple(mcrlrecord, tuple(lock, tuple(undefined, tuple(nil, tuplenil(nil))))) |
| record_extract(tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2))))), lock, resource) | → | tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2))))) | | record_update(tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2))))), lock, pending, NewF) | → | tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(NewF))))) |
| record_updates(Record, Name, nil) | → | Record | | record_updates(Record, Name, cons(tuple(Field, tuplenil(NewF)), Fields)) | → | record_updates(record_update(Record, Name, Field, NewF), Name, Fields) |
| locker2_map_promote_pending(nil, Pending) | → | nil | | locker2_map_promote_pending(cons(Lock, Locks), Pending) | → | cons(locker2_promote_pending(Lock, Pending), locker2_map_promote_pending(Locks, Pending)) |
| locker2_map_claim_lock(nil, Resources, Client) | → | nil | | locker2_map_claim_lock(cons(Lock, Locks), Resources, Client) | → | cons(locker2_claim_lock(Lock, Resources, Client), locker2_map_claim_lock(Locks, Resources, Client)) |
| locker2_map_add_pending(nil, Resources, Client) | → | nil | | locker2_promote_pending(Lock, Client) | → | case0(Client, Lock, record_extract(Lock, lock, pending)) |
| case0(Client, Lock, cons(Client, Pendings)) | → | record_updates(Lock, lock, cons(tuple(excl, tuplenil(Client)), cons(tuple(pending, tuplenil(Pendings)), nil))) | | case0(Client, Lock, MCRLFree0) | → | Lock |
| locker2_remove_pending(Lock, Client) | → | record_updates(Lock, lock, cons(tuple(pending, tuplenil(subtract(record_extract(Lock, lock, pending), cons(Client, nil)))), nil)) | | locker2_add_pending(Lock, Resources, Client) | → | case1(Client, Resources, Lock, member(record_extract(Lock, lock, resource), Resources)) |
| case1(Client, Resources, Lock, true) | → | record_updates(Lock, lock, cons(tuple(pending, tuplenil(append(record_extract(Lock, lock, pending), cons(Client, nil)))), nil)) | | case1(Client, Resources, Lock, false) | → | Lock |
| locker2_release_lock(Lock, Client) | → | case2(Client, Lock, gen_modtageq(Client, record_extract(Lock, lock, excl))) | | case2(Client, Lock, true) | → | record_updates(Lock, lock, cons(tuple(excllock, excl), nil)) |
| case4(Client, Lock, MCRLFree1) | → | false | | locker2_obtainables(nil, Client) | → | true |
| locker2_obtainables(cons(Lock, Locks), Client) | → | case5(Client, Locks, Lock, member(Client, record_extract(Lock, lock, pending))) | | case5(Client, Locks, Lock, true) | → | andt(locker2_obtainable(Lock, Client), locker2_obtainables(Locks, Client)) |
| case5(Client, Locks, Lock, false) | → | locker2_obtainables(Locks, Client) | | locker2_check_available(Resource, nil) | → | false |
| locker2_check_available(Resource, cons(Lock, Locks)) | → | case6(Locks, Lock, Resource, equal(Resource, record_extract(Lock, lock, resource))) | | case6(Locks, Lock, Resource, true) | → | andt(equal(record_extract(Lock, lock, excl), nil), equal(record_extract(Lock, lock, pending), nil)) |
| case6(Locks, Lock, Resource, false) | → | locker2_check_available(Resource, Locks) | | locker2_check_availables(nil, Locks) | → | true |
| locker2_check_availables(cons(Resource, Resources), Locks) | → | andt(locker2_check_available(Resource, Locks), locker2_check_availables(Resources, Locks)) | | locker2_adduniq(nil, List) | → | List |
| append(cons(Head, Tail), List) | → | cons(Head, append(Tail, List)) | | subtract(List, nil) | → | List |
| subtract(List, cons(Head, Tail)) | → | subtract(delete(Head, List), Tail) | | delete(E, nil) | → | nil |
| delete(E, cons(Head, Tail)) | → | case8(Tail, Head, E, equal(E, Head)) | | case8(Tail, Head, E, true) | → | Tail |
| case8(Tail, Head, E, false) | → | cons(Head, delete(E, Tail)) | | gen_tag(Pid) | → | tuple(Pid, tuplenil(tag)) |
| gen_modtageq(Client1, Client2) | → | equal(Client1, Client2) | | member(E, nil) | → | false |
| member(E, cons(Head, Tail)) | → | case9(Tail, Head, E, equal(E, Head)) | | case9(Tail, Head, E, true) | → | true |
| case9(Tail, Head, E, false) | → | member(E, Tail) | | eqs(empty, empty) | → | T |
| eqs(empty, stack(E2, S2)) | → | F | | eqs(stack(E1, S1), empty) | → | F |
| eqs(stack(E1, S1), stack(E2, S2)) | → | and(eqt(E1, E2), eqs(S1, S2)) | | pushs(E1, S1) | → | stack(E1, S1) |
| pops(stack(E1, S1)) | → | S1 | | tops(stack(E1, S1)) | → | E1 |
| istops(E1, empty) | → | F | | istops(E1, stack(E2, S1)) | → | eqt(E1, E2) |
| eqc(nocalls, nocalls) | → | T | | eqc(nocalls, calls(E2, S2, CS2)) | → | F |
| eqc(calls(E1, S1, CS1), nocalls) | → | F | | eqc(calls(E1, S1, CS1), calls(E2, S2, CS2)) | → | and(eqt(E1, E2), and(eqs(S1, S2), eqc(CS1, CS2))) |
| push(E1, E2, nocalls) | → | calls(E1, stack(E2, empty), nocalls) | | push(E1, E2, calls(E3, S1, CS1)) | → | push1(E1, E2, E3, S1, CS1, eqt(E1, E3)) |
| push1(E1, E2, E3, S1, CS1, T) | → | calls(E3, pushs(E2, S1), CS1) |
Original Signature
Termination of terms over the following signature is verified: tuplenil, record_new, tuple, tag, gen_tag, imp, locker2_map_promote_pending, pops, locker2_check_availables, mcrlrecord, pending, request, empty, false, ok, istops, locker2_add_pending, andt, case2, append, element, case1, case0, tops, push1, case6, case5, or, int, case4, record_extract, locker, case9, case8, locker2_map_add_pending, calls, eqc, and, not, 0, locker2_promote_pending, locker2_claim_lock, locker2_adduniq, stack, release, locker2_obtainables, F, locker2_remove_pending, push, T, gen_modtageq, record_update, undefined, if, record_updates, eqt, excllock, delete, eqs, cons, member, locker2_map_claim_lock, locker2_obtainable, a, pushs, resource, lock, true, locker2_release_lock, pid, equal, subtract, locker2_check_available, s, excl, nil, eq, nocalls
Strategy
Projection
The following projection was used:
Thus, the following dependency pairs are removed:
| eqc#(calls(E1, S1, CS1), calls(E2, S2, CS2)) | → | eqc#(CS1, CS2) |
Problem 8: SubtermCriterion
Dependency Pair Problem
Dependency Pairs
| locker2_check_availables#(cons(Resource, Resources), Locks) | → | locker2_check_availables#(Resources, Locks) |
Rewrite Rules
| or(T, T) | → | T | | or(F, T) | → | T |
| or(T, F) | → | T | | or(F, F) | → | F |
| and(T, B) | → | B | | and(B, T) | → | B |
| and(F, B) | → | F | | and(B, F) | → | F |
| imp(T, B) | → | B | | imp(F, B) | → | T |
| not(T) | → | F | | not(F) | → | T |
| if(T, B1, B2) | → | B1 | | if(F, B1, B2) | → | B2 |
| eq(T, T) | → | T | | eq(F, F) | → | T |
| eq(T, F) | → | F | | eq(F, T) | → | F |
| eqt(nil, undefined) | → | F | | eqt(nil, pid(N2)) | → | F |
| eqt(nil, int(N2)) | → | F | | eqt(nil, cons(H2, T2)) | → | F |
| eqt(nil, tuple(H2, T2)) | → | F | | eqt(nil, tuplenil(H2)) | → | F |
| eqt(a, nil) | → | F | | eqt(a, a) | → | T |
| eqt(a, excl) | → | F | | eqt(a, false) | → | F |
| eqt(a, lock) | → | F | | eqt(a, locker) | → | F |
| eqt(a, mcrlrecord) | → | F | | eqt(a, ok) | → | F |
| eqt(a, pending) | → | F | | eqt(a, release) | → | F |
| eqt(a, request) | → | F | | eqt(a, resource) | → | F |
| eqt(a, tag) | → | F | | eqt(a, true) | → | F |
| eqt(a, undefined) | → | F | | eqt(a, pid(N2)) | → | F |
| eqt(a, int(N2)) | → | F | | eqt(a, cons(H2, T2)) | → | F |
| eqt(a, tuple(H2, T2)) | → | F | | eqt(a, tuplenil(H2)) | → | F |
| eqt(excl, nil) | → | F | | eqt(excl, a) | → | F |
| eqt(excl, excl) | → | T | | eqt(excl, false) | → | F |
| eqt(excl, lock) | → | F | | eqt(excl, locker) | → | F |
| eqt(excl, mcrlrecord) | → | F | | eqt(excl, ok) | → | F |
| eqt(excl, pending) | → | F | | eqt(excl, release) | → | F |
| eqt(excl, request) | → | F | | eqt(excl, resource) | → | F |
| eqt(excl, tag) | → | F | | eqt(excl, true) | → | F |
| eqt(excl, undefined) | → | F | | eqt(excl, pid(N2)) | → | F |
| eqt(excl, eqt(false, int(N2))) | → | F | | eqt(false, cons(H2, T2)) | → | F |
| eqt(false, tuple(H2, T2)) | → | F | | eqt(false, tuplenil(H2)) | → | F |
| eqt(lock, nil) | → | F | | eqt(lock, a) | → | F |
| eqt(lock, excl) | → | F | | eqt(lock, false) | → | F |
| eqt(lock, lock) | → | T | | eqt(lock, locker) | → | F |
| eqt(lock, mcrlrecord) | → | F | | eqt(lock, ok) | → | F |
| eqt(lock, pending) | → | F | | eqt(lock, release) | → | F |
| eqt(lock, request) | → | F | | eqt(lock, resource) | → | F |
| eqt(lock, tag) | → | F | | eqt(lock, true) | → | F |
| eqt(lock, undefined) | → | F | | eqt(lock, pid(N2)) | → | F |
| eqt(lock, int(N2)) | → | F | | eqt(lock, cons(H2, T2)) | → | F |
| eqt(lock, tuple(H2, T2)) | → | F | | eqt(lock, tuplenil(H2)) | → | F |
| eqt(locker, nil) | → | F | | eqt(locker, a) | → | F |
| eqt(locker, excl) | → | F | | eqt(locker, false) | → | F |
| eqt(locker, lock) | → | F | | eqt(locker, locker) | → | T |
| eqt(locker, mcrlrecord) | → | F | | eqt(locker, ok) | → | F |
| eqt(locker, pending) | → | F | | eqt(locker, release) | → | F |
| eqt(locker, request) | → | F | | eqt(locker, resource) | → | F |
| eqt(locker, tag) | → | F | | eqt(locker, true) | → | F |
| eqt(locker, undefined) | → | F | | eqt(locker, pid(N2)) | → | F |
| eqt(locker, int(N2)) | → | F | | eqt(locker, cons(H2, T2)) | → | F |
| eqt(locker, tuple(H2, T2)) | → | F | | eqt(locker, tuplenil(H2)) | → | F |
| eqt(mcrlrecord, nil) | → | F | | eqt(mcrlrecord, a) | → | F |
| eqt(mcrlrecord, excl) | → | F | | eqt(mcrlrecord, false) | → | F |
| eqt(mcrlrecord, lock) | → | F | | eqt(mcrlrecord, locker) | → | F |
| eqt(mcrlrecord, mcrlrecord) | → | T | | eqt(mcrlrecord, ok) | → | F |
| eqt(mcrlrecord, pending) | → | F | | eqt(mcrlrecord, release) | → | F |
| eqt(mcrlrecord, request) | → | F | | eqt(mcrlrecord, resource) | → | F |
| eqt(ok, resource) | → | F | | eqt(ok, tag) | → | F |
| eqt(ok, true) | → | F | | eqt(ok, undefined) | → | F |
| eqt(ok, pid(N2)) | → | F | | eqt(ok, int(N2)) | → | F |
| eqt(ok, cons(H2, T2)) | → | F | | eqt(ok, tuple(H2, T2)) | → | F |
| eqt(ok, tuplenil(H2)) | → | F | | eqt(pending, nil) | → | F |
| eqt(pending, a) | → | F | | eqt(pending, excl) | → | F |
| eqt(pending, false) | → | F | | eqt(pending, lock) | → | F |
| eqt(pending, locker) | → | F | | eqt(pending, mcrlrecord) | → | F |
| eqt(pending, ok) | → | F | | eqt(pending, pending) | → | T |
| eqt(pending, release) | → | F | | eqt(pending, request) | → | F |
| eqt(pending, resource) | → | F | | eqt(pending, tag) | → | F |
| eqt(pending, true) | → | F | | eqt(pending, undefined) | → | F |
| eqt(pending, pid(N2)) | → | F | | eqt(pending, int(N2)) | → | F |
| eqt(pending, cons(H2, T2)) | → | F | | eqt(pending, tuple(H2, T2)) | → | F |
| eqt(pending, tuplenil(H2)) | → | F | | eqt(release, nil) | → | F |
| eqt(release, a) | → | F | | eqt(release, excl) | → | F |
| eqt(release, false) | → | F | | eqt(release, lock) | → | F |
| eqt(release, locker) | → | F | | eqt(release, mcrlrecord) | → | F |
| eqt(release, ok) | → | F | | eqt(request, mcrlrecord) | → | F |
| eqt(request, ok) | → | F | | eqt(request, pending) | → | F |
| eqt(request, release) | → | F | | eqt(request, request) | → | T |
| eqt(request, resource) | → | F | | eqt(request, tag) | → | F |
| eqt(request, true) | → | F | | eqt(request, undefined) | → | F |
| eqt(request, pid(N2)) | → | F | | eqt(request, int(N2)) | → | F |
| eqt(request, cons(H2, T2)) | → | F | | eqt(request, tuple(H2, T2)) | → | F |
| eqt(request, tuplenil(H2)) | → | F | | eqt(resource, nil) | → | F |
| eqt(resource, a) | → | F | | eqt(resource, excl) | → | F |
| eqt(resource, false) | → | F | | eqt(resource, lock) | → | F |
| eqt(resource, locker) | → | F | | eqt(resource, mcrlrecord) | → | F |
| eqt(resource, ok) | → | F | | eqt(resource, pending) | → | F |
| eqt(resource, release) | → | F | | eqt(resource, request) | → | F |
| eqt(resource, resource) | → | T | | eqt(resource, tag) | → | F |
| eqt(resource, true) | → | F | | eqt(resource, undefined) | → | F |
| eqt(resource, pid(N2)) | → | F | | eqt(resource, int(N2)) | → | F |
| eqt(resource, cons(H2, T2)) | → | F | | eqt(resource, tuple(H2, T2)) | → | F |
| eqt(resource, tuplenil(H2)) | → | F | | eqt(tag, nil) | → | F |
| eqt(tag, a) | → | F | | eqt(tag, excl) | → | F |
| eqt(tag, false) | → | F | | eqt(tag, lock) | → | F |
| eqt(tag, locker) | → | F | | eqt(tag, mcrlrecord) | → | F |
| eqt(tag, ok) | → | F | | eqt(tag, pending) | → | F |
| eqt(tag, release) | → | F | | eqt(tag, request) | → | F |
| eqt(tag, resource) | → | F | | eqt(tag, tag) | → | T |
| eqt(tag, true) | → | F | | eqt(tag, undefined) | → | F |
| eqt(tag, pid(N2)) | → | F | | eqt(tag, int(N2)) | → | F |
| eqt(tag, cons(H2, T2)) | → | F | | eqt(tag, tuple(H2, T2)) | → | F |
| eqt(tag, tuplenil(H2)) | → | F | | eqt(true, nil) | → | F |
| eqt(true, a) | → | F | | eqt(true, excl) | → | F |
| eqt(true, false) | → | F | | eqt(true, lock) | → | F |
| eqt(true, locker) | → | F | | eqt(true, mcrlrecord) | → | F |
| eqt(true, ok) | → | F | | eqt(true, pending) | → | F |
| eqt(true, release) | → | F | | eqt(true, request) | → | F |
| eqt(true, resource) | → | F | | eqt(true, tag) | → | F |
| eqt(true, true) | → | T | | eqt(true, undefined) | → | F |
| eqt(true, pid(N2)) | → | F | | eqt(true, int(N2)) | → | F |
| eqt(true, cons(H2, T2)) | → | F | | eqt(true, tuple(H2, T2)) | → | F |
| eqt(true, tuplenil(H2)) | → | F | | eqt(undefined, nil) | → | F |
| eqt(undefined, a) | → | F | | eqt(undefined, tuplenil(H2)) | → | F |
| eqt(pid(N1), nil) | → | F | | eqt(pid(N1), a) | → | F |
| eqt(pid(N1), excl) | → | F | | eqt(pid(N1), false) | → | F |
| eqt(pid(N1), lock) | → | F | | eqt(pid(N1), locker) | → | F |
| eqt(pid(N1), mcrlrecord) | → | F | | eqt(pid(N1), ok) | → | F |
| eqt(pid(N1), pending) | → | F | | eqt(pid(N1), release) | → | F |
| eqt(pid(N1), request) | → | F | | eqt(pid(N1), resource) | → | F |
| eqt(pid(N1), tag) | → | F | | eqt(pid(N1), true) | → | F |
| eqt(pid(N1), undefined) | → | F | | eqt(pid(N1), pid(N2)) | → | eqt(N1, N2) |
| eqt(pid(N1), int(N2)) | → | F | | eqt(pid(N1), cons(H2, T2)) | → | F |
| eqt(pid(N1), tuple(H2, T2)) | → | F | | eqt(pid(N1), tuplenil(H2)) | → | F |
| eqt(int(N1), nil) | → | F | | eqt(int(N1), a) | → | F |
| eqt(int(N1), excl) | → | F | | eqt(int(N1), false) | → | F |
| eqt(int(N1), lock) | → | F | | eqt(int(N1), locker) | → | F |
| eqt(int(N1), mcrlrecord) | → | F | | eqt(int(N1), ok) | → | F |
| eqt(int(N1), pending) | → | F | | eqt(int(N1), release) | → | F |
| eqt(int(N1), request) | → | F | | eqt(int(N1), resource) | → | F |
| eqt(int(N1), tag) | → | F | | eqt(int(N1), true) | → | F |
| eqt(int(N1), undefined) | → | F | | eqt(cons(H1, T1), resource) | → | F |
| eqt(cons(H1, T1), tag) | → | F | | eqt(cons(H1, T1), true) | → | F |
| eqt(cons(H1, T1), undefined) | → | F | | eqt(cons(H1, T1), pid(N2)) | → | F |
| eqt(cons(H1, T1), int(N2)) | → | F | | eqt(cons(H1, T1), cons(H2, T2)) | → | and(eqt(H1, H2), eqt(T1, T2)) |
| eqt(cons(H1, T1), tuple(H2, T2)) | → | F | | eqt(cons(H1, T1), tuplenil(H2)) | → | F |
| eqt(tuple(H1, T1), nil) | → | F | | eqt(tuple(H1, T1), a) | → | F |
| eqt(tuple(H1, T1), excl) | → | F | | eqt(tuple(H1, T1), false) | → | F |
| eqt(tuple(H1, T1), lock) | → | F | | eqt(tuple(H1, T1), locker) | → | F |
| eqt(tuple(H1, T1), mcrlrecord) | → | F | | eqt(tuple(H1, T1), ok) | → | F |
| eqt(tuple(H1, T1), pending) | → | F | | eqt(tuple(H1, T1), release) | → | F |
| eqt(tuple(H1, T1), request) | → | F | | eqt(tuple(H1, T1), resource) | → | F |
| eqt(tuple(H1, T1), tag) | → | F | | eqt(tuple(H1, T1), true) | → | F |
| eqt(tuple(H1, T1), undefined) | → | F | | eqt(tuple(H1, T1), pid(N2)) | → | F |
| eqt(tuple(H1, T1), int(N2)) | → | F | | eqt(tuple(H1, T1), cons(H2, T2)) | → | F |
| eqt(tuple(H1, T1), tuple(H2, T2)) | → | and(eqt(H1, H2), eqt(T1, T2)) | | eqt(tuple(H1, T1), tuplenil(H2)) | → | F |
| eqt(tuplenil(H1), nil) | → | F | | eqt(tuplenil(H1), a) | → | F |
| eqt(tuplenil(H1), excl) | → | F | | eqt(tuplenil(H1), false) | → | F |
| eqt(tuplenil(H1), lock) | → | F | | eqt(tuplenil(H1), locker) | → | F |
| eqt(tuplenil(H1), mcrlrecord) | → | F | | eqt(tuplenil(H1), ok) | → | F |
| eqt(tuplenil(H1), pending) | → | F | | eqt(tuplenil(H1), release) | → | F |
| eqt(tuplenil(H1), request) | → | F | | eqt(tuplenil(H1), resource) | → | F |
| eqt(tuplenil(H1), tag) | → | F | | eqt(tuplenil(H1), true) | → | F |
| eqt(tuplenil(H1), undefined) | → | F | | eqt(tuplenil(H1), pid(N2)) | → | F |
| eqt(tuplenil(H1), int(N2)) | → | F | | eqt(tuplenil(H1), cons(H2, T2)) | → | F |
| eqt(tuplenil(H1), tuple(H2, T2)) | → | F | | eqt(tuplenil(H1), tuplenil(H2)) | → | eqt(H1, H2) |
| element(int(s(0)), tuplenil(T1)) | → | T1 | | element(int(s(0)), tuple(T1, T2)) | → | T1 |
| element(int(s(s(N1))), tuple(T1, T2)) | → | element(int(s(N1)), T2) | | record_new(lock) | → | tuple(mcrlrecord, tuple(lock, tuple(undefined, tuple(nil, tuplenil(nil))))) |
| record_extract(tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2))))), lock, resource) | → | tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2))))) | | record_update(tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2))))), lock, pending, NewF) | → | tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(NewF))))) |
| record_updates(Record, Name, nil) | → | Record | | record_updates(Record, Name, cons(tuple(Field, tuplenil(NewF)), Fields)) | → | record_updates(record_update(Record, Name, Field, NewF), Name, Fields) |
| locker2_map_promote_pending(nil, Pending) | → | nil | | locker2_map_promote_pending(cons(Lock, Locks), Pending) | → | cons(locker2_promote_pending(Lock, Pending), locker2_map_promote_pending(Locks, Pending)) |
| locker2_map_claim_lock(nil, Resources, Client) | → | nil | | locker2_map_claim_lock(cons(Lock, Locks), Resources, Client) | → | cons(locker2_claim_lock(Lock, Resources, Client), locker2_map_claim_lock(Locks, Resources, Client)) |
| locker2_map_add_pending(nil, Resources, Client) | → | nil | | locker2_promote_pending(Lock, Client) | → | case0(Client, Lock, record_extract(Lock, lock, pending)) |
| case0(Client, Lock, cons(Client, Pendings)) | → | record_updates(Lock, lock, cons(tuple(excl, tuplenil(Client)), cons(tuple(pending, tuplenil(Pendings)), nil))) | | case0(Client, Lock, MCRLFree0) | → | Lock |
| locker2_remove_pending(Lock, Client) | → | record_updates(Lock, lock, cons(tuple(pending, tuplenil(subtract(record_extract(Lock, lock, pending), cons(Client, nil)))), nil)) | | locker2_add_pending(Lock, Resources, Client) | → | case1(Client, Resources, Lock, member(record_extract(Lock, lock, resource), Resources)) |
| case1(Client, Resources, Lock, true) | → | record_updates(Lock, lock, cons(tuple(pending, tuplenil(append(record_extract(Lock, lock, pending), cons(Client, nil)))), nil)) | | case1(Client, Resources, Lock, false) | → | Lock |
| locker2_release_lock(Lock, Client) | → | case2(Client, Lock, gen_modtageq(Client, record_extract(Lock, lock, excl))) | | case2(Client, Lock, true) | → | record_updates(Lock, lock, cons(tuple(excllock, excl), nil)) |
| case4(Client, Lock, MCRLFree1) | → | false | | locker2_obtainables(nil, Client) | → | true |
| locker2_obtainables(cons(Lock, Locks), Client) | → | case5(Client, Locks, Lock, member(Client, record_extract(Lock, lock, pending))) | | case5(Client, Locks, Lock, true) | → | andt(locker2_obtainable(Lock, Client), locker2_obtainables(Locks, Client)) |
| case5(Client, Locks, Lock, false) | → | locker2_obtainables(Locks, Client) | | locker2_check_available(Resource, nil) | → | false |
| locker2_check_available(Resource, cons(Lock, Locks)) | → | case6(Locks, Lock, Resource, equal(Resource, record_extract(Lock, lock, resource))) | | case6(Locks, Lock, Resource, true) | → | andt(equal(record_extract(Lock, lock, excl), nil), equal(record_extract(Lock, lock, pending), nil)) |
| case6(Locks, Lock, Resource, false) | → | locker2_check_available(Resource, Locks) | | locker2_check_availables(nil, Locks) | → | true |
| locker2_check_availables(cons(Resource, Resources), Locks) | → | andt(locker2_check_available(Resource, Locks), locker2_check_availables(Resources, Locks)) | | locker2_adduniq(nil, List) | → | List |
| append(cons(Head, Tail), List) | → | cons(Head, append(Tail, List)) | | subtract(List, nil) | → | List |
| subtract(List, cons(Head, Tail)) | → | subtract(delete(Head, List), Tail) | | delete(E, nil) | → | nil |
| delete(E, cons(Head, Tail)) | → | case8(Tail, Head, E, equal(E, Head)) | | case8(Tail, Head, E, true) | → | Tail |
| case8(Tail, Head, E, false) | → | cons(Head, delete(E, Tail)) | | gen_tag(Pid) | → | tuple(Pid, tuplenil(tag)) |
| gen_modtageq(Client1, Client2) | → | equal(Client1, Client2) | | member(E, nil) | → | false |
| member(E, cons(Head, Tail)) | → | case9(Tail, Head, E, equal(E, Head)) | | case9(Tail, Head, E, true) | → | true |
| case9(Tail, Head, E, false) | → | member(E, Tail) | | eqs(empty, empty) | → | T |
| eqs(empty, stack(E2, S2)) | → | F | | eqs(stack(E1, S1), empty) | → | F |
| eqs(stack(E1, S1), stack(E2, S2)) | → | and(eqt(E1, E2), eqs(S1, S2)) | | pushs(E1, S1) | → | stack(E1, S1) |
| pops(stack(E1, S1)) | → | S1 | | tops(stack(E1, S1)) | → | E1 |
| istops(E1, empty) | → | F | | istops(E1, stack(E2, S1)) | → | eqt(E1, E2) |
| eqc(nocalls, nocalls) | → | T | | eqc(nocalls, calls(E2, S2, CS2)) | → | F |
| eqc(calls(E1, S1, CS1), nocalls) | → | F | | eqc(calls(E1, S1, CS1), calls(E2, S2, CS2)) | → | and(eqt(E1, E2), and(eqs(S1, S2), eqc(CS1, CS2))) |
| push(E1, E2, nocalls) | → | calls(E1, stack(E2, empty), nocalls) | | push(E1, E2, calls(E3, S1, CS1)) | → | push1(E1, E2, E3, S1, CS1, eqt(E1, E3)) |
| push1(E1, E2, E3, S1, CS1, T) | → | calls(E3, pushs(E2, S1), CS1) |
Original Signature
Termination of terms over the following signature is verified: tuplenil, record_new, tuple, tag, gen_tag, imp, locker2_map_promote_pending, pops, locker2_check_availables, mcrlrecord, pending, request, empty, false, ok, istops, locker2_add_pending, andt, case2, append, element, case1, case0, tops, push1, case6, case5, or, int, case4, record_extract, locker, case9, case8, locker2_map_add_pending, calls, eqc, and, not, 0, locker2_promote_pending, locker2_claim_lock, locker2_adduniq, stack, release, locker2_obtainables, F, locker2_remove_pending, push, T, gen_modtageq, record_update, undefined, if, record_updates, eqt, excllock, delete, eqs, cons, member, locker2_map_claim_lock, locker2_obtainable, a, pushs, resource, lock, true, locker2_release_lock, pid, equal, subtract, locker2_check_available, s, excl, nil, eq, nocalls
Strategy
Projection
The following projection was used:
- π (locker2_check_availables#): 1
Thus, the following dependency pairs are removed:
| locker2_check_availables#(cons(Resource, Resources), Locks) | → | locker2_check_availables#(Resources, Locks) |
Problem 9: SubtermCriterion
Dependency Pair Problem
Dependency Pairs
| eqs#(stack(E1, S1), stack(E2, S2)) | → | eqs#(S1, S2) |
Rewrite Rules
| or(T, T) | → | T | | or(F, T) | → | T |
| or(T, F) | → | T | | or(F, F) | → | F |
| and(T, B) | → | B | | and(B, T) | → | B |
| and(F, B) | → | F | | and(B, F) | → | F |
| imp(T, B) | → | B | | imp(F, B) | → | T |
| not(T) | → | F | | not(F) | → | T |
| if(T, B1, B2) | → | B1 | | if(F, B1, B2) | → | B2 |
| eq(T, T) | → | T | | eq(F, F) | → | T |
| eq(T, F) | → | F | | eq(F, T) | → | F |
| eqt(nil, undefined) | → | F | | eqt(nil, pid(N2)) | → | F |
| eqt(nil, int(N2)) | → | F | | eqt(nil, cons(H2, T2)) | → | F |
| eqt(nil, tuple(H2, T2)) | → | F | | eqt(nil, tuplenil(H2)) | → | F |
| eqt(a, nil) | → | F | | eqt(a, a) | → | T |
| eqt(a, excl) | → | F | | eqt(a, false) | → | F |
| eqt(a, lock) | → | F | | eqt(a, locker) | → | F |
| eqt(a, mcrlrecord) | → | F | | eqt(a, ok) | → | F |
| eqt(a, pending) | → | F | | eqt(a, release) | → | F |
| eqt(a, request) | → | F | | eqt(a, resource) | → | F |
| eqt(a, tag) | → | F | | eqt(a, true) | → | F |
| eqt(a, undefined) | → | F | | eqt(a, pid(N2)) | → | F |
| eqt(a, int(N2)) | → | F | | eqt(a, cons(H2, T2)) | → | F |
| eqt(a, tuple(H2, T2)) | → | F | | eqt(a, tuplenil(H2)) | → | F |
| eqt(excl, nil) | → | F | | eqt(excl, a) | → | F |
| eqt(excl, excl) | → | T | | eqt(excl, false) | → | F |
| eqt(excl, lock) | → | F | | eqt(excl, locker) | → | F |
| eqt(excl, mcrlrecord) | → | F | | eqt(excl, ok) | → | F |
| eqt(excl, pending) | → | F | | eqt(excl, release) | → | F |
| eqt(excl, request) | → | F | | eqt(excl, resource) | → | F |
| eqt(excl, tag) | → | F | | eqt(excl, true) | → | F |
| eqt(excl, undefined) | → | F | | eqt(excl, pid(N2)) | → | F |
| eqt(excl, eqt(false, int(N2))) | → | F | | eqt(false, cons(H2, T2)) | → | F |
| eqt(false, tuple(H2, T2)) | → | F | | eqt(false, tuplenil(H2)) | → | F |
| eqt(lock, nil) | → | F | | eqt(lock, a) | → | F |
| eqt(lock, excl) | → | F | | eqt(lock, false) | → | F |
| eqt(lock, lock) | → | T | | eqt(lock, locker) | → | F |
| eqt(lock, mcrlrecord) | → | F | | eqt(lock, ok) | → | F |
| eqt(lock, pending) | → | F | | eqt(lock, release) | → | F |
| eqt(lock, request) | → | F | | eqt(lock, resource) | → | F |
| eqt(lock, tag) | → | F | | eqt(lock, true) | → | F |
| eqt(lock, undefined) | → | F | | eqt(lock, pid(N2)) | → | F |
| eqt(lock, int(N2)) | → | F | | eqt(lock, cons(H2, T2)) | → | F |
| eqt(lock, tuple(H2, T2)) | → | F | | eqt(lock, tuplenil(H2)) | → | F |
| eqt(locker, nil) | → | F | | eqt(locker, a) | → | F |
| eqt(locker, excl) | → | F | | eqt(locker, false) | → | F |
| eqt(locker, lock) | → | F | | eqt(locker, locker) | → | T |
| eqt(locker, mcrlrecord) | → | F | | eqt(locker, ok) | → | F |
| eqt(locker, pending) | → | F | | eqt(locker, release) | → | F |
| eqt(locker, request) | → | F | | eqt(locker, resource) | → | F |
| eqt(locker, tag) | → | F | | eqt(locker, true) | → | F |
| eqt(locker, undefined) | → | F | | eqt(locker, pid(N2)) | → | F |
| eqt(locker, int(N2)) | → | F | | eqt(locker, cons(H2, T2)) | → | F |
| eqt(locker, tuple(H2, T2)) | → | F | | eqt(locker, tuplenil(H2)) | → | F |
| eqt(mcrlrecord, nil) | → | F | | eqt(mcrlrecord, a) | → | F |
| eqt(mcrlrecord, excl) | → | F | | eqt(mcrlrecord, false) | → | F |
| eqt(mcrlrecord, lock) | → | F | | eqt(mcrlrecord, locker) | → | F |
| eqt(mcrlrecord, mcrlrecord) | → | T | | eqt(mcrlrecord, ok) | → | F |
| eqt(mcrlrecord, pending) | → | F | | eqt(mcrlrecord, release) | → | F |
| eqt(mcrlrecord, request) | → | F | | eqt(mcrlrecord, resource) | → | F |
| eqt(ok, resource) | → | F | | eqt(ok, tag) | → | F |
| eqt(ok, true) | → | F | | eqt(ok, undefined) | → | F |
| eqt(ok, pid(N2)) | → | F | | eqt(ok, int(N2)) | → | F |
| eqt(ok, cons(H2, T2)) | → | F | | eqt(ok, tuple(H2, T2)) | → | F |
| eqt(ok, tuplenil(H2)) | → | F | | eqt(pending, nil) | → | F |
| eqt(pending, a) | → | F | | eqt(pending, excl) | → | F |
| eqt(pending, false) | → | F | | eqt(pending, lock) | → | F |
| eqt(pending, locker) | → | F | | eqt(pending, mcrlrecord) | → | F |
| eqt(pending, ok) | → | F | | eqt(pending, pending) | → | T |
| eqt(pending, release) | → | F | | eqt(pending, request) | → | F |
| eqt(pending, resource) | → | F | | eqt(pending, tag) | → | F |
| eqt(pending, true) | → | F | | eqt(pending, undefined) | → | F |
| eqt(pending, pid(N2)) | → | F | | eqt(pending, int(N2)) | → | F |
| eqt(pending, cons(H2, T2)) | → | F | | eqt(pending, tuple(H2, T2)) | → | F |
| eqt(pending, tuplenil(H2)) | → | F | | eqt(release, nil) | → | F |
| eqt(release, a) | → | F | | eqt(release, excl) | → | F |
| eqt(release, false) | → | F | | eqt(release, lock) | → | F |
| eqt(release, locker) | → | F | | eqt(release, mcrlrecord) | → | F |
| eqt(release, ok) | → | F | | eqt(request, mcrlrecord) | → | F |
| eqt(request, ok) | → | F | | eqt(request, pending) | → | F |
| eqt(request, release) | → | F | | eqt(request, request) | → | T |
| eqt(request, resource) | → | F | | eqt(request, tag) | → | F |
| eqt(request, true) | → | F | | eqt(request, undefined) | → | F |
| eqt(request, pid(N2)) | → | F | | eqt(request, int(N2)) | → | F |
| eqt(request, cons(H2, T2)) | → | F | | eqt(request, tuple(H2, T2)) | → | F |
| eqt(request, tuplenil(H2)) | → | F | | eqt(resource, nil) | → | F |
| eqt(resource, a) | → | F | | eqt(resource, excl) | → | F |
| eqt(resource, false) | → | F | | eqt(resource, lock) | → | F |
| eqt(resource, locker) | → | F | | eqt(resource, mcrlrecord) | → | F |
| eqt(resource, ok) | → | F | | eqt(resource, pending) | → | F |
| eqt(resource, release) | → | F | | eqt(resource, request) | → | F |
| eqt(resource, resource) | → | T | | eqt(resource, tag) | → | F |
| eqt(resource, true) | → | F | | eqt(resource, undefined) | → | F |
| eqt(resource, pid(N2)) | → | F | | eqt(resource, int(N2)) | → | F |
| eqt(resource, cons(H2, T2)) | → | F | | eqt(resource, tuple(H2, T2)) | → | F |
| eqt(resource, tuplenil(H2)) | → | F | | eqt(tag, nil) | → | F |
| eqt(tag, a) | → | F | | eqt(tag, excl) | → | F |
| eqt(tag, false) | → | F | | eqt(tag, lock) | → | F |
| eqt(tag, locker) | → | F | | eqt(tag, mcrlrecord) | → | F |
| eqt(tag, ok) | → | F | | eqt(tag, pending) | → | F |
| eqt(tag, release) | → | F | | eqt(tag, request) | → | F |
| eqt(tag, resource) | → | F | | eqt(tag, tag) | → | T |
| eqt(tag, true) | → | F | | eqt(tag, undefined) | → | F |
| eqt(tag, pid(N2)) | → | F | | eqt(tag, int(N2)) | → | F |
| eqt(tag, cons(H2, T2)) | → | F | | eqt(tag, tuple(H2, T2)) | → | F |
| eqt(tag, tuplenil(H2)) | → | F | | eqt(true, nil) | → | F |
| eqt(true, a) | → | F | | eqt(true, excl) | → | F |
| eqt(true, false) | → | F | | eqt(true, lock) | → | F |
| eqt(true, locker) | → | F | | eqt(true, mcrlrecord) | → | F |
| eqt(true, ok) | → | F | | eqt(true, pending) | → | F |
| eqt(true, release) | → | F | | eqt(true, request) | → | F |
| eqt(true, resource) | → | F | | eqt(true, tag) | → | F |
| eqt(true, true) | → | T | | eqt(true, undefined) | → | F |
| eqt(true, pid(N2)) | → | F | | eqt(true, int(N2)) | → | F |
| eqt(true, cons(H2, T2)) | → | F | | eqt(true, tuple(H2, T2)) | → | F |
| eqt(true, tuplenil(H2)) | → | F | | eqt(undefined, nil) | → | F |
| eqt(undefined, a) | → | F | | eqt(undefined, tuplenil(H2)) | → | F |
| eqt(pid(N1), nil) | → | F | | eqt(pid(N1), a) | → | F |
| eqt(pid(N1), excl) | → | F | | eqt(pid(N1), false) | → | F |
| eqt(pid(N1), lock) | → | F | | eqt(pid(N1), locker) | → | F |
| eqt(pid(N1), mcrlrecord) | → | F | | eqt(pid(N1), ok) | → | F |
| eqt(pid(N1), pending) | → | F | | eqt(pid(N1), release) | → | F |
| eqt(pid(N1), request) | → | F | | eqt(pid(N1), resource) | → | F |
| eqt(pid(N1), tag) | → | F | | eqt(pid(N1), true) | → | F |
| eqt(pid(N1), undefined) | → | F | | eqt(pid(N1), pid(N2)) | → | eqt(N1, N2) |
| eqt(pid(N1), int(N2)) | → | F | | eqt(pid(N1), cons(H2, T2)) | → | F |
| eqt(pid(N1), tuple(H2, T2)) | → | F | | eqt(pid(N1), tuplenil(H2)) | → | F |
| eqt(int(N1), nil) | → | F | | eqt(int(N1), a) | → | F |
| eqt(int(N1), excl) | → | F | | eqt(int(N1), false) | → | F |
| eqt(int(N1), lock) | → | F | | eqt(int(N1), locker) | → | F |
| eqt(int(N1), mcrlrecord) | → | F | | eqt(int(N1), ok) | → | F |
| eqt(int(N1), pending) | → | F | | eqt(int(N1), release) | → | F |
| eqt(int(N1), request) | → | F | | eqt(int(N1), resource) | → | F |
| eqt(int(N1), tag) | → | F | | eqt(int(N1), true) | → | F |
| eqt(int(N1), undefined) | → | F | | eqt(cons(H1, T1), resource) | → | F |
| eqt(cons(H1, T1), tag) | → | F | | eqt(cons(H1, T1), true) | → | F |
| eqt(cons(H1, T1), undefined) | → | F | | eqt(cons(H1, T1), pid(N2)) | → | F |
| eqt(cons(H1, T1), int(N2)) | → | F | | eqt(cons(H1, T1), cons(H2, T2)) | → | and(eqt(H1, H2), eqt(T1, T2)) |
| eqt(cons(H1, T1), tuple(H2, T2)) | → | F | | eqt(cons(H1, T1), tuplenil(H2)) | → | F |
| eqt(tuple(H1, T1), nil) | → | F | | eqt(tuple(H1, T1), a) | → | F |
| eqt(tuple(H1, T1), excl) | → | F | | eqt(tuple(H1, T1), false) | → | F |
| eqt(tuple(H1, T1), lock) | → | F | | eqt(tuple(H1, T1), locker) | → | F |
| eqt(tuple(H1, T1), mcrlrecord) | → | F | | eqt(tuple(H1, T1), ok) | → | F |
| eqt(tuple(H1, T1), pending) | → | F | | eqt(tuple(H1, T1), release) | → | F |
| eqt(tuple(H1, T1), request) | → | F | | eqt(tuple(H1, T1), resource) | → | F |
| eqt(tuple(H1, T1), tag) | → | F | | eqt(tuple(H1, T1), true) | → | F |
| eqt(tuple(H1, T1), undefined) | → | F | | eqt(tuple(H1, T1), pid(N2)) | → | F |
| eqt(tuple(H1, T1), int(N2)) | → | F | | eqt(tuple(H1, T1), cons(H2, T2)) | → | F |
| eqt(tuple(H1, T1), tuple(H2, T2)) | → | and(eqt(H1, H2), eqt(T1, T2)) | | eqt(tuple(H1, T1), tuplenil(H2)) | → | F |
| eqt(tuplenil(H1), nil) | → | F | | eqt(tuplenil(H1), a) | → | F |
| eqt(tuplenil(H1), excl) | → | F | | eqt(tuplenil(H1), false) | → | F |
| eqt(tuplenil(H1), lock) | → | F | | eqt(tuplenil(H1), locker) | → | F |
| eqt(tuplenil(H1), mcrlrecord) | → | F | | eqt(tuplenil(H1), ok) | → | F |
| eqt(tuplenil(H1), pending) | → | F | | eqt(tuplenil(H1), release) | → | F |
| eqt(tuplenil(H1), request) | → | F | | eqt(tuplenil(H1), resource) | → | F |
| eqt(tuplenil(H1), tag) | → | F | | eqt(tuplenil(H1), true) | → | F |
| eqt(tuplenil(H1), undefined) | → | F | | eqt(tuplenil(H1), pid(N2)) | → | F |
| eqt(tuplenil(H1), int(N2)) | → | F | | eqt(tuplenil(H1), cons(H2, T2)) | → | F |
| eqt(tuplenil(H1), tuple(H2, T2)) | → | F | | eqt(tuplenil(H1), tuplenil(H2)) | → | eqt(H1, H2) |
| element(int(s(0)), tuplenil(T1)) | → | T1 | | element(int(s(0)), tuple(T1, T2)) | → | T1 |
| element(int(s(s(N1))), tuple(T1, T2)) | → | element(int(s(N1)), T2) | | record_new(lock) | → | tuple(mcrlrecord, tuple(lock, tuple(undefined, tuple(nil, tuplenil(nil))))) |
| record_extract(tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2))))), lock, resource) | → | tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2))))) | | record_update(tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2))))), lock, pending, NewF) | → | tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(NewF))))) |
| record_updates(Record, Name, nil) | → | Record | | record_updates(Record, Name, cons(tuple(Field, tuplenil(NewF)), Fields)) | → | record_updates(record_update(Record, Name, Field, NewF), Name, Fields) |
| locker2_map_promote_pending(nil, Pending) | → | nil | | locker2_map_promote_pending(cons(Lock, Locks), Pending) | → | cons(locker2_promote_pending(Lock, Pending), locker2_map_promote_pending(Locks, Pending)) |
| locker2_map_claim_lock(nil, Resources, Client) | → | nil | | locker2_map_claim_lock(cons(Lock, Locks), Resources, Client) | → | cons(locker2_claim_lock(Lock, Resources, Client), locker2_map_claim_lock(Locks, Resources, Client)) |
| locker2_map_add_pending(nil, Resources, Client) | → | nil | | locker2_promote_pending(Lock, Client) | → | case0(Client, Lock, record_extract(Lock, lock, pending)) |
| case0(Client, Lock, cons(Client, Pendings)) | → | record_updates(Lock, lock, cons(tuple(excl, tuplenil(Client)), cons(tuple(pending, tuplenil(Pendings)), nil))) | | case0(Client, Lock, MCRLFree0) | → | Lock |
| locker2_remove_pending(Lock, Client) | → | record_updates(Lock, lock, cons(tuple(pending, tuplenil(subtract(record_extract(Lock, lock, pending), cons(Client, nil)))), nil)) | | locker2_add_pending(Lock, Resources, Client) | → | case1(Client, Resources, Lock, member(record_extract(Lock, lock, resource), Resources)) |
| case1(Client, Resources, Lock, true) | → | record_updates(Lock, lock, cons(tuple(pending, tuplenil(append(record_extract(Lock, lock, pending), cons(Client, nil)))), nil)) | | case1(Client, Resources, Lock, false) | → | Lock |
| locker2_release_lock(Lock, Client) | → | case2(Client, Lock, gen_modtageq(Client, record_extract(Lock, lock, excl))) | | case2(Client, Lock, true) | → | record_updates(Lock, lock, cons(tuple(excllock, excl), nil)) |
| case4(Client, Lock, MCRLFree1) | → | false | | locker2_obtainables(nil, Client) | → | true |
| locker2_obtainables(cons(Lock, Locks), Client) | → | case5(Client, Locks, Lock, member(Client, record_extract(Lock, lock, pending))) | | case5(Client, Locks, Lock, true) | → | andt(locker2_obtainable(Lock, Client), locker2_obtainables(Locks, Client)) |
| case5(Client, Locks, Lock, false) | → | locker2_obtainables(Locks, Client) | | locker2_check_available(Resource, nil) | → | false |
| locker2_check_available(Resource, cons(Lock, Locks)) | → | case6(Locks, Lock, Resource, equal(Resource, record_extract(Lock, lock, resource))) | | case6(Locks, Lock, Resource, true) | → | andt(equal(record_extract(Lock, lock, excl), nil), equal(record_extract(Lock, lock, pending), nil)) |
| case6(Locks, Lock, Resource, false) | → | locker2_check_available(Resource, Locks) | | locker2_check_availables(nil, Locks) | → | true |
| locker2_check_availables(cons(Resource, Resources), Locks) | → | andt(locker2_check_available(Resource, Locks), locker2_check_availables(Resources, Locks)) | | locker2_adduniq(nil, List) | → | List |
| append(cons(Head, Tail), List) | → | cons(Head, append(Tail, List)) | | subtract(List, nil) | → | List |
| subtract(List, cons(Head, Tail)) | → | subtract(delete(Head, List), Tail) | | delete(E, nil) | → | nil |
| delete(E, cons(Head, Tail)) | → | case8(Tail, Head, E, equal(E, Head)) | | case8(Tail, Head, E, true) | → | Tail |
| case8(Tail, Head, E, false) | → | cons(Head, delete(E, Tail)) | | gen_tag(Pid) | → | tuple(Pid, tuplenil(tag)) |
| gen_modtageq(Client1, Client2) | → | equal(Client1, Client2) | | member(E, nil) | → | false |
| member(E, cons(Head, Tail)) | → | case9(Tail, Head, E, equal(E, Head)) | | case9(Tail, Head, E, true) | → | true |
| case9(Tail, Head, E, false) | → | member(E, Tail) | | eqs(empty, empty) | → | T |
| eqs(empty, stack(E2, S2)) | → | F | | eqs(stack(E1, S1), empty) | → | F |
| eqs(stack(E1, S1), stack(E2, S2)) | → | and(eqt(E1, E2), eqs(S1, S2)) | | pushs(E1, S1) | → | stack(E1, S1) |
| pops(stack(E1, S1)) | → | S1 | | tops(stack(E1, S1)) | → | E1 |
| istops(E1, empty) | → | F | | istops(E1, stack(E2, S1)) | → | eqt(E1, E2) |
| eqc(nocalls, nocalls) | → | T | | eqc(nocalls, calls(E2, S2, CS2)) | → | F |
| eqc(calls(E1, S1, CS1), nocalls) | → | F | | eqc(calls(E1, S1, CS1), calls(E2, S2, CS2)) | → | and(eqt(E1, E2), and(eqs(S1, S2), eqc(CS1, CS2))) |
| push(E1, E2, nocalls) | → | calls(E1, stack(E2, empty), nocalls) | | push(E1, E2, calls(E3, S1, CS1)) | → | push1(E1, E2, E3, S1, CS1, eqt(E1, E3)) |
| push1(E1, E2, E3, S1, CS1, T) | → | calls(E3, pushs(E2, S1), CS1) |
Original Signature
Termination of terms over the following signature is verified: tuplenil, record_new, tuple, tag, gen_tag, imp, locker2_map_promote_pending, pops, locker2_check_availables, mcrlrecord, pending, request, empty, false, ok, istops, locker2_add_pending, andt, case2, append, element, case1, case0, tops, push1, case6, case5, or, int, case4, record_extract, locker, case9, case8, locker2_map_add_pending, calls, eqc, and, not, 0, locker2_promote_pending, locker2_claim_lock, locker2_adduniq, stack, release, locker2_obtainables, F, locker2_remove_pending, push, T, gen_modtageq, record_update, undefined, if, record_updates, eqt, excllock, delete, eqs, cons, member, locker2_map_claim_lock, locker2_obtainable, a, pushs, resource, lock, true, locker2_release_lock, pid, equal, subtract, locker2_check_available, s, excl, nil, eq, nocalls
Strategy
Projection
The following projection was used:
Thus, the following dependency pairs are removed:
| eqs#(stack(E1, S1), stack(E2, S2)) | → | eqs#(S1, S2) |
Problem 10: SubtermCriterion
Dependency Pair Problem
Dependency Pairs
| eqt#(pid(N1), pid(N2)) | → | eqt#(N1, N2) | | eqt#(tuple(H1, T1), tuple(H2, T2)) | → | eqt#(T1, T2) |
| eqt#(tuple(H1, T1), tuple(H2, T2)) | → | eqt#(H1, H2) | | eqt#(cons(H1, T1), cons(H2, T2)) | → | eqt#(H1, H2) |
| eqt#(tuplenil(H1), tuplenil(H2)) | → | eqt#(H1, H2) | | eqt#(cons(H1, T1), cons(H2, T2)) | → | eqt#(T1, T2) |
Rewrite Rules
| or(T, T) | → | T | | or(F, T) | → | T |
| or(T, F) | → | T | | or(F, F) | → | F |
| and(T, B) | → | B | | and(B, T) | → | B |
| and(F, B) | → | F | | and(B, F) | → | F |
| imp(T, B) | → | B | | imp(F, B) | → | T |
| not(T) | → | F | | not(F) | → | T |
| if(T, B1, B2) | → | B1 | | if(F, B1, B2) | → | B2 |
| eq(T, T) | → | T | | eq(F, F) | → | T |
| eq(T, F) | → | F | | eq(F, T) | → | F |
| eqt(nil, undefined) | → | F | | eqt(nil, pid(N2)) | → | F |
| eqt(nil, int(N2)) | → | F | | eqt(nil, cons(H2, T2)) | → | F |
| eqt(nil, tuple(H2, T2)) | → | F | | eqt(nil, tuplenil(H2)) | → | F |
| eqt(a, nil) | → | F | | eqt(a, a) | → | T |
| eqt(a, excl) | → | F | | eqt(a, false) | → | F |
| eqt(a, lock) | → | F | | eqt(a, locker) | → | F |
| eqt(a, mcrlrecord) | → | F | | eqt(a, ok) | → | F |
| eqt(a, pending) | → | F | | eqt(a, release) | → | F |
| eqt(a, request) | → | F | | eqt(a, resource) | → | F |
| eqt(a, tag) | → | F | | eqt(a, true) | → | F |
| eqt(a, undefined) | → | F | | eqt(a, pid(N2)) | → | F |
| eqt(a, int(N2)) | → | F | | eqt(a, cons(H2, T2)) | → | F |
| eqt(a, tuple(H2, T2)) | → | F | | eqt(a, tuplenil(H2)) | → | F |
| eqt(excl, nil) | → | F | | eqt(excl, a) | → | F |
| eqt(excl, excl) | → | T | | eqt(excl, false) | → | F |
| eqt(excl, lock) | → | F | | eqt(excl, locker) | → | F |
| eqt(excl, mcrlrecord) | → | F | | eqt(excl, ok) | → | F |
| eqt(excl, pending) | → | F | | eqt(excl, release) | → | F |
| eqt(excl, request) | → | F | | eqt(excl, resource) | → | F |
| eqt(excl, tag) | → | F | | eqt(excl, true) | → | F |
| eqt(excl, undefined) | → | F | | eqt(excl, pid(N2)) | → | F |
| eqt(excl, eqt(false, int(N2))) | → | F | | eqt(false, cons(H2, T2)) | → | F |
| eqt(false, tuple(H2, T2)) | → | F | | eqt(false, tuplenil(H2)) | → | F |
| eqt(lock, nil) | → | F | | eqt(lock, a) | → | F |
| eqt(lock, excl) | → | F | | eqt(lock, false) | → | F |
| eqt(lock, lock) | → | T | | eqt(lock, locker) | → | F |
| eqt(lock, mcrlrecord) | → | F | | eqt(lock, ok) | → | F |
| eqt(lock, pending) | → | F | | eqt(lock, release) | → | F |
| eqt(lock, request) | → | F | | eqt(lock, resource) | → | F |
| eqt(lock, tag) | → | F | | eqt(lock, true) | → | F |
| eqt(lock, undefined) | → | F | | eqt(lock, pid(N2)) | → | F |
| eqt(lock, int(N2)) | → | F | | eqt(lock, cons(H2, T2)) | → | F |
| eqt(lock, tuple(H2, T2)) | → | F | | eqt(lock, tuplenil(H2)) | → | F |
| eqt(locker, nil) | → | F | | eqt(locker, a) | → | F |
| eqt(locker, excl) | → | F | | eqt(locker, false) | → | F |
| eqt(locker, lock) | → | F | | eqt(locker, locker) | → | T |
| eqt(locker, mcrlrecord) | → | F | | eqt(locker, ok) | → | F |
| eqt(locker, pending) | → | F | | eqt(locker, release) | → | F |
| eqt(locker, request) | → | F | | eqt(locker, resource) | → | F |
| eqt(locker, tag) | → | F | | eqt(locker, true) | → | F |
| eqt(locker, undefined) | → | F | | eqt(locker, pid(N2)) | → | F |
| eqt(locker, int(N2)) | → | F | | eqt(locker, cons(H2, T2)) | → | F |
| eqt(locker, tuple(H2, T2)) | → | F | | eqt(locker, tuplenil(H2)) | → | F |
| eqt(mcrlrecord, nil) | → | F | | eqt(mcrlrecord, a) | → | F |
| eqt(mcrlrecord, excl) | → | F | | eqt(mcrlrecord, false) | → | F |
| eqt(mcrlrecord, lock) | → | F | | eqt(mcrlrecord, locker) | → | F |
| eqt(mcrlrecord, mcrlrecord) | → | T | | eqt(mcrlrecord, ok) | → | F |
| eqt(mcrlrecord, pending) | → | F | | eqt(mcrlrecord, release) | → | F |
| eqt(mcrlrecord, request) | → | F | | eqt(mcrlrecord, resource) | → | F |
| eqt(ok, resource) | → | F | | eqt(ok, tag) | → | F |
| eqt(ok, true) | → | F | | eqt(ok, undefined) | → | F |
| eqt(ok, pid(N2)) | → | F | | eqt(ok, int(N2)) | → | F |
| eqt(ok, cons(H2, T2)) | → | F | | eqt(ok, tuple(H2, T2)) | → | F |
| eqt(ok, tuplenil(H2)) | → | F | | eqt(pending, nil) | → | F |
| eqt(pending, a) | → | F | | eqt(pending, excl) | → | F |
| eqt(pending, false) | → | F | | eqt(pending, lock) | → | F |
| eqt(pending, locker) | → | F | | eqt(pending, mcrlrecord) | → | F |
| eqt(pending, ok) | → | F | | eqt(pending, pending) | → | T |
| eqt(pending, release) | → | F | | eqt(pending, request) | → | F |
| eqt(pending, resource) | → | F | | eqt(pending, tag) | → | F |
| eqt(pending, true) | → | F | | eqt(pending, undefined) | → | F |
| eqt(pending, pid(N2)) | → | F | | eqt(pending, int(N2)) | → | F |
| eqt(pending, cons(H2, T2)) | → | F | | eqt(pending, tuple(H2, T2)) | → | F |
| eqt(pending, tuplenil(H2)) | → | F | | eqt(release, nil) | → | F |
| eqt(release, a) | → | F | | eqt(release, excl) | → | F |
| eqt(release, false) | → | F | | eqt(release, lock) | → | F |
| eqt(release, locker) | → | F | | eqt(release, mcrlrecord) | → | F |
| eqt(release, ok) | → | F | | eqt(request, mcrlrecord) | → | F |
| eqt(request, ok) | → | F | | eqt(request, pending) | → | F |
| eqt(request, release) | → | F | | eqt(request, request) | → | T |
| eqt(request, resource) | → | F | | eqt(request, tag) | → | F |
| eqt(request, true) | → | F | | eqt(request, undefined) | → | F |
| eqt(request, pid(N2)) | → | F | | eqt(request, int(N2)) | → | F |
| eqt(request, cons(H2, T2)) | → | F | | eqt(request, tuple(H2, T2)) | → | F |
| eqt(request, tuplenil(H2)) | → | F | | eqt(resource, nil) | → | F |
| eqt(resource, a) | → | F | | eqt(resource, excl) | → | F |
| eqt(resource, false) | → | F | | eqt(resource, lock) | → | F |
| eqt(resource, locker) | → | F | | eqt(resource, mcrlrecord) | → | F |
| eqt(resource, ok) | → | F | | eqt(resource, pending) | → | F |
| eqt(resource, release) | → | F | | eqt(resource, request) | → | F |
| eqt(resource, resource) | → | T | | eqt(resource, tag) | → | F |
| eqt(resource, true) | → | F | | eqt(resource, undefined) | → | F |
| eqt(resource, pid(N2)) | → | F | | eqt(resource, int(N2)) | → | F |
| eqt(resource, cons(H2, T2)) | → | F | | eqt(resource, tuple(H2, T2)) | → | F |
| eqt(resource, tuplenil(H2)) | → | F | | eqt(tag, nil) | → | F |
| eqt(tag, a) | → | F | | eqt(tag, excl) | → | F |
| eqt(tag, false) | → | F | | eqt(tag, lock) | → | F |
| eqt(tag, locker) | → | F | | eqt(tag, mcrlrecord) | → | F |
| eqt(tag, ok) | → | F | | eqt(tag, pending) | → | F |
| eqt(tag, release) | → | F | | eqt(tag, request) | → | F |
| eqt(tag, resource) | → | F | | eqt(tag, tag) | → | T |
| eqt(tag, true) | → | F | | eqt(tag, undefined) | → | F |
| eqt(tag, pid(N2)) | → | F | | eqt(tag, int(N2)) | → | F |
| eqt(tag, cons(H2, T2)) | → | F | | eqt(tag, tuple(H2, T2)) | → | F |
| eqt(tag, tuplenil(H2)) | → | F | | eqt(true, nil) | → | F |
| eqt(true, a) | → | F | | eqt(true, excl) | → | F |
| eqt(true, false) | → | F | | eqt(true, lock) | → | F |
| eqt(true, locker) | → | F | | eqt(true, mcrlrecord) | → | F |
| eqt(true, ok) | → | F | | eqt(true, pending) | → | F |
| eqt(true, release) | → | F | | eqt(true, request) | → | F |
| eqt(true, resource) | → | F | | eqt(true, tag) | → | F |
| eqt(true, true) | → | T | | eqt(true, undefined) | → | F |
| eqt(true, pid(N2)) | → | F | | eqt(true, int(N2)) | → | F |
| eqt(true, cons(H2, T2)) | → | F | | eqt(true, tuple(H2, T2)) | → | F |
| eqt(true, tuplenil(H2)) | → | F | | eqt(undefined, nil) | → | F |
| eqt(undefined, a) | → | F | | eqt(undefined, tuplenil(H2)) | → | F |
| eqt(pid(N1), nil) | → | F | | eqt(pid(N1), a) | → | F |
| eqt(pid(N1), excl) | → | F | | eqt(pid(N1), false) | → | F |
| eqt(pid(N1), lock) | → | F | | eqt(pid(N1), locker) | → | F |
| eqt(pid(N1), mcrlrecord) | → | F | | eqt(pid(N1), ok) | → | F |
| eqt(pid(N1), pending) | → | F | | eqt(pid(N1), release) | → | F |
| eqt(pid(N1), request) | → | F | | eqt(pid(N1), resource) | → | F |
| eqt(pid(N1), tag) | → | F | | eqt(pid(N1), true) | → | F |
| eqt(pid(N1), undefined) | → | F | | eqt(pid(N1), pid(N2)) | → | eqt(N1, N2) |
| eqt(pid(N1), int(N2)) | → | F | | eqt(pid(N1), cons(H2, T2)) | → | F |
| eqt(pid(N1), tuple(H2, T2)) | → | F | | eqt(pid(N1), tuplenil(H2)) | → | F |
| eqt(int(N1), nil) | → | F | | eqt(int(N1), a) | → | F |
| eqt(int(N1), excl) | → | F | | eqt(int(N1), false) | → | F |
| eqt(int(N1), lock) | → | F | | eqt(int(N1), locker) | → | F |
| eqt(int(N1), mcrlrecord) | → | F | | eqt(int(N1), ok) | → | F |
| eqt(int(N1), pending) | → | F | | eqt(int(N1), release) | → | F |
| eqt(int(N1), request) | → | F | | eqt(int(N1), resource) | → | F |
| eqt(int(N1), tag) | → | F | | eqt(int(N1), true) | → | F |
| eqt(int(N1), undefined) | → | F | | eqt(cons(H1, T1), resource) | → | F |
| eqt(cons(H1, T1), tag) | → | F | | eqt(cons(H1, T1), true) | → | F |
| eqt(cons(H1, T1), undefined) | → | F | | eqt(cons(H1, T1), pid(N2)) | → | F |
| eqt(cons(H1, T1), int(N2)) | → | F | | eqt(cons(H1, T1), cons(H2, T2)) | → | and(eqt(H1, H2), eqt(T1, T2)) |
| eqt(cons(H1, T1), tuple(H2, T2)) | → | F | | eqt(cons(H1, T1), tuplenil(H2)) | → | F |
| eqt(tuple(H1, T1), nil) | → | F | | eqt(tuple(H1, T1), a) | → | F |
| eqt(tuple(H1, T1), excl) | → | F | | eqt(tuple(H1, T1), false) | → | F |
| eqt(tuple(H1, T1), lock) | → | F | | eqt(tuple(H1, T1), locker) | → | F |
| eqt(tuple(H1, T1), mcrlrecord) | → | F | | eqt(tuple(H1, T1), ok) | → | F |
| eqt(tuple(H1, T1), pending) | → | F | | eqt(tuple(H1, T1), release) | → | F |
| eqt(tuple(H1, T1), request) | → | F | | eqt(tuple(H1, T1), resource) | → | F |
| eqt(tuple(H1, T1), tag) | → | F | | eqt(tuple(H1, T1), true) | → | F |
| eqt(tuple(H1, T1), undefined) | → | F | | eqt(tuple(H1, T1), pid(N2)) | → | F |
| eqt(tuple(H1, T1), int(N2)) | → | F | | eqt(tuple(H1, T1), cons(H2, T2)) | → | F |
| eqt(tuple(H1, T1), tuple(H2, T2)) | → | and(eqt(H1, H2), eqt(T1, T2)) | | eqt(tuple(H1, T1), tuplenil(H2)) | → | F |
| eqt(tuplenil(H1), nil) | → | F | | eqt(tuplenil(H1), a) | → | F |
| eqt(tuplenil(H1), excl) | → | F | | eqt(tuplenil(H1), false) | → | F |
| eqt(tuplenil(H1), lock) | → | F | | eqt(tuplenil(H1), locker) | → | F |
| eqt(tuplenil(H1), mcrlrecord) | → | F | | eqt(tuplenil(H1), ok) | → | F |
| eqt(tuplenil(H1), pending) | → | F | | eqt(tuplenil(H1), release) | → | F |
| eqt(tuplenil(H1), request) | → | F | | eqt(tuplenil(H1), resource) | → | F |
| eqt(tuplenil(H1), tag) | → | F | | eqt(tuplenil(H1), true) | → | F |
| eqt(tuplenil(H1), undefined) | → | F | | eqt(tuplenil(H1), pid(N2)) | → | F |
| eqt(tuplenil(H1), int(N2)) | → | F | | eqt(tuplenil(H1), cons(H2, T2)) | → | F |
| eqt(tuplenil(H1), tuple(H2, T2)) | → | F | | eqt(tuplenil(H1), tuplenil(H2)) | → | eqt(H1, H2) |
| element(int(s(0)), tuplenil(T1)) | → | T1 | | element(int(s(0)), tuple(T1, T2)) | → | T1 |
| element(int(s(s(N1))), tuple(T1, T2)) | → | element(int(s(N1)), T2) | | record_new(lock) | → | tuple(mcrlrecord, tuple(lock, tuple(undefined, tuple(nil, tuplenil(nil))))) |
| record_extract(tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2))))), lock, resource) | → | tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2))))) | | record_update(tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2))))), lock, pending, NewF) | → | tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(NewF))))) |
| record_updates(Record, Name, nil) | → | Record | | record_updates(Record, Name, cons(tuple(Field, tuplenil(NewF)), Fields)) | → | record_updates(record_update(Record, Name, Field, NewF), Name, Fields) |
| locker2_map_promote_pending(nil, Pending) | → | nil | | locker2_map_promote_pending(cons(Lock, Locks), Pending) | → | cons(locker2_promote_pending(Lock, Pending), locker2_map_promote_pending(Locks, Pending)) |
| locker2_map_claim_lock(nil, Resources, Client) | → | nil | | locker2_map_claim_lock(cons(Lock, Locks), Resources, Client) | → | cons(locker2_claim_lock(Lock, Resources, Client), locker2_map_claim_lock(Locks, Resources, Client)) |
| locker2_map_add_pending(nil, Resources, Client) | → | nil | | locker2_promote_pending(Lock, Client) | → | case0(Client, Lock, record_extract(Lock, lock, pending)) |
| case0(Client, Lock, cons(Client, Pendings)) | → | record_updates(Lock, lock, cons(tuple(excl, tuplenil(Client)), cons(tuple(pending, tuplenil(Pendings)), nil))) | | case0(Client, Lock, MCRLFree0) | → | Lock |
| locker2_remove_pending(Lock, Client) | → | record_updates(Lock, lock, cons(tuple(pending, tuplenil(subtract(record_extract(Lock, lock, pending), cons(Client, nil)))), nil)) | | locker2_add_pending(Lock, Resources, Client) | → | case1(Client, Resources, Lock, member(record_extract(Lock, lock, resource), Resources)) |
| case1(Client, Resources, Lock, true) | → | record_updates(Lock, lock, cons(tuple(pending, tuplenil(append(record_extract(Lock, lock, pending), cons(Client, nil)))), nil)) | | case1(Client, Resources, Lock, false) | → | Lock |
| locker2_release_lock(Lock, Client) | → | case2(Client, Lock, gen_modtageq(Client, record_extract(Lock, lock, excl))) | | case2(Client, Lock, true) | → | record_updates(Lock, lock, cons(tuple(excllock, excl), nil)) |
| case4(Client, Lock, MCRLFree1) | → | false | | locker2_obtainables(nil, Client) | → | true |
| locker2_obtainables(cons(Lock, Locks), Client) | → | case5(Client, Locks, Lock, member(Client, record_extract(Lock, lock, pending))) | | case5(Client, Locks, Lock, true) | → | andt(locker2_obtainable(Lock, Client), locker2_obtainables(Locks, Client)) |
| case5(Client, Locks, Lock, false) | → | locker2_obtainables(Locks, Client) | | locker2_check_available(Resource, nil) | → | false |
| locker2_check_available(Resource, cons(Lock, Locks)) | → | case6(Locks, Lock, Resource, equal(Resource, record_extract(Lock, lock, resource))) | | case6(Locks, Lock, Resource, true) | → | andt(equal(record_extract(Lock, lock, excl), nil), equal(record_extract(Lock, lock, pending), nil)) |
| case6(Locks, Lock, Resource, false) | → | locker2_check_available(Resource, Locks) | | locker2_check_availables(nil, Locks) | → | true |
| locker2_check_availables(cons(Resource, Resources), Locks) | → | andt(locker2_check_available(Resource, Locks), locker2_check_availables(Resources, Locks)) | | locker2_adduniq(nil, List) | → | List |
| append(cons(Head, Tail), List) | → | cons(Head, append(Tail, List)) | | subtract(List, nil) | → | List |
| subtract(List, cons(Head, Tail)) | → | subtract(delete(Head, List), Tail) | | delete(E, nil) | → | nil |
| delete(E, cons(Head, Tail)) | → | case8(Tail, Head, E, equal(E, Head)) | | case8(Tail, Head, E, true) | → | Tail |
| case8(Tail, Head, E, false) | → | cons(Head, delete(E, Tail)) | | gen_tag(Pid) | → | tuple(Pid, tuplenil(tag)) |
| gen_modtageq(Client1, Client2) | → | equal(Client1, Client2) | | member(E, nil) | → | false |
| member(E, cons(Head, Tail)) | → | case9(Tail, Head, E, equal(E, Head)) | | case9(Tail, Head, E, true) | → | true |
| case9(Tail, Head, E, false) | → | member(E, Tail) | | eqs(empty, empty) | → | T |
| eqs(empty, stack(E2, S2)) | → | F | | eqs(stack(E1, S1), empty) | → | F |
| eqs(stack(E1, S1), stack(E2, S2)) | → | and(eqt(E1, E2), eqs(S1, S2)) | | pushs(E1, S1) | → | stack(E1, S1) |
| pops(stack(E1, S1)) | → | S1 | | tops(stack(E1, S1)) | → | E1 |
| istops(E1, empty) | → | F | | istops(E1, stack(E2, S1)) | → | eqt(E1, E2) |
| eqc(nocalls, nocalls) | → | T | | eqc(nocalls, calls(E2, S2, CS2)) | → | F |
| eqc(calls(E1, S1, CS1), nocalls) | → | F | | eqc(calls(E1, S1, CS1), calls(E2, S2, CS2)) | → | and(eqt(E1, E2), and(eqs(S1, S2), eqc(CS1, CS2))) |
| push(E1, E2, nocalls) | → | calls(E1, stack(E2, empty), nocalls) | | push(E1, E2, calls(E3, S1, CS1)) | → | push1(E1, E2, E3, S1, CS1, eqt(E1, E3)) |
| push1(E1, E2, E3, S1, CS1, T) | → | calls(E3, pushs(E2, S1), CS1) |
Original Signature
Termination of terms over the following signature is verified: tuplenil, record_new, tuple, tag, gen_tag, imp, locker2_map_promote_pending, pops, locker2_check_availables, mcrlrecord, pending, request, empty, false, ok, istops, locker2_add_pending, andt, case2, append, element, case1, case0, tops, push1, case6, case5, or, int, case4, record_extract, locker, case9, case8, locker2_map_add_pending, calls, eqc, and, not, 0, locker2_promote_pending, locker2_claim_lock, locker2_adduniq, stack, release, locker2_obtainables, F, locker2_remove_pending, push, T, gen_modtageq, record_update, undefined, if, record_updates, eqt, excllock, delete, eqs, cons, member, locker2_map_claim_lock, locker2_obtainable, a, pushs, resource, lock, true, locker2_release_lock, pid, equal, subtract, locker2_check_available, s, excl, nil, eq, nocalls
Strategy
Projection
The following projection was used:
Thus, the following dependency pairs are removed:
| eqt#(pid(N1), pid(N2)) | → | eqt#(N1, N2) | | eqt#(tuple(H1, T1), tuple(H2, T2)) | → | eqt#(T1, T2) |
| eqt#(cons(H1, T1), cons(H2, T2)) | → | eqt#(H1, H2) | | eqt#(tuple(H1, T1), tuple(H2, T2)) | → | eqt#(H1, H2) |
| eqt#(tuplenil(H1), tuplenil(H2)) | → | eqt#(H1, H2) | | eqt#(cons(H1, T1), cons(H2, T2)) | → | eqt#(T1, T2) |
Problem 11: SubtermCriterion
Dependency Pair Problem
Dependency Pairs
| record_updates#(Record, Name, cons(tuple(Field, tuplenil(NewF)), Fields)) | → | record_updates#(record_update(Record, Name, Field, NewF), Name, Fields) |
Rewrite Rules
| or(T, T) | → | T | | or(F, T) | → | T |
| or(T, F) | → | T | | or(F, F) | → | F |
| and(T, B) | → | B | | and(B, T) | → | B |
| and(F, B) | → | F | | and(B, F) | → | F |
| imp(T, B) | → | B | | imp(F, B) | → | T |
| not(T) | → | F | | not(F) | → | T |
| if(T, B1, B2) | → | B1 | | if(F, B1, B2) | → | B2 |
| eq(T, T) | → | T | | eq(F, F) | → | T |
| eq(T, F) | → | F | | eq(F, T) | → | F |
| eqt(nil, undefined) | → | F | | eqt(nil, pid(N2)) | → | F |
| eqt(nil, int(N2)) | → | F | | eqt(nil, cons(H2, T2)) | → | F |
| eqt(nil, tuple(H2, T2)) | → | F | | eqt(nil, tuplenil(H2)) | → | F |
| eqt(a, nil) | → | F | | eqt(a, a) | → | T |
| eqt(a, excl) | → | F | | eqt(a, false) | → | F |
| eqt(a, lock) | → | F | | eqt(a, locker) | → | F |
| eqt(a, mcrlrecord) | → | F | | eqt(a, ok) | → | F |
| eqt(a, pending) | → | F | | eqt(a, release) | → | F |
| eqt(a, request) | → | F | | eqt(a, resource) | → | F |
| eqt(a, tag) | → | F | | eqt(a, true) | → | F |
| eqt(a, undefined) | → | F | | eqt(a, pid(N2)) | → | F |
| eqt(a, int(N2)) | → | F | | eqt(a, cons(H2, T2)) | → | F |
| eqt(a, tuple(H2, T2)) | → | F | | eqt(a, tuplenil(H2)) | → | F |
| eqt(excl, nil) | → | F | | eqt(excl, a) | → | F |
| eqt(excl, excl) | → | T | | eqt(excl, false) | → | F |
| eqt(excl, lock) | → | F | | eqt(excl, locker) | → | F |
| eqt(excl, mcrlrecord) | → | F | | eqt(excl, ok) | → | F |
| eqt(excl, pending) | → | F | | eqt(excl, release) | → | F |
| eqt(excl, request) | → | F | | eqt(excl, resource) | → | F |
| eqt(excl, tag) | → | F | | eqt(excl, true) | → | F |
| eqt(excl, undefined) | → | F | | eqt(excl, pid(N2)) | → | F |
| eqt(excl, eqt(false, int(N2))) | → | F | | eqt(false, cons(H2, T2)) | → | F |
| eqt(false, tuple(H2, T2)) | → | F | | eqt(false, tuplenil(H2)) | → | F |
| eqt(lock, nil) | → | F | | eqt(lock, a) | → | F |
| eqt(lock, excl) | → | F | | eqt(lock, false) | → | F |
| eqt(lock, lock) | → | T | | eqt(lock, locker) | → | F |
| eqt(lock, mcrlrecord) | → | F | | eqt(lock, ok) | → | F |
| eqt(lock, pending) | → | F | | eqt(lock, release) | → | F |
| eqt(lock, request) | → | F | | eqt(lock, resource) | → | F |
| eqt(lock, tag) | → | F | | eqt(lock, true) | → | F |
| eqt(lock, undefined) | → | F | | eqt(lock, pid(N2)) | → | F |
| eqt(lock, int(N2)) | → | F | | eqt(lock, cons(H2, T2)) | → | F |
| eqt(lock, tuple(H2, T2)) | → | F | | eqt(lock, tuplenil(H2)) | → | F |
| eqt(locker, nil) | → | F | | eqt(locker, a) | → | F |
| eqt(locker, excl) | → | F | | eqt(locker, false) | → | F |
| eqt(locker, lock) | → | F | | eqt(locker, locker) | → | T |
| eqt(locker, mcrlrecord) | → | F | | eqt(locker, ok) | → | F |
| eqt(locker, pending) | → | F | | eqt(locker, release) | → | F |
| eqt(locker, request) | → | F | | eqt(locker, resource) | → | F |
| eqt(locker, tag) | → | F | | eqt(locker, true) | → | F |
| eqt(locker, undefined) | → | F | | eqt(locker, pid(N2)) | → | F |
| eqt(locker, int(N2)) | → | F | | eqt(locker, cons(H2, T2)) | → | F |
| eqt(locker, tuple(H2, T2)) | → | F | | eqt(locker, tuplenil(H2)) | → | F |
| eqt(mcrlrecord, nil) | → | F | | eqt(mcrlrecord, a) | → | F |
| eqt(mcrlrecord, excl) | → | F | | eqt(mcrlrecord, false) | → | F |
| eqt(mcrlrecord, lock) | → | F | | eqt(mcrlrecord, locker) | → | F |
| eqt(mcrlrecord, mcrlrecord) | → | T | | eqt(mcrlrecord, ok) | → | F |
| eqt(mcrlrecord, pending) | → | F | | eqt(mcrlrecord, release) | → | F |
| eqt(mcrlrecord, request) | → | F | | eqt(mcrlrecord, resource) | → | F |
| eqt(ok, resource) | → | F | | eqt(ok, tag) | → | F |
| eqt(ok, true) | → | F | | eqt(ok, undefined) | → | F |
| eqt(ok, pid(N2)) | → | F | | eqt(ok, int(N2)) | → | F |
| eqt(ok, cons(H2, T2)) | → | F | | eqt(ok, tuple(H2, T2)) | → | F |
| eqt(ok, tuplenil(H2)) | → | F | | eqt(pending, nil) | → | F |
| eqt(pending, a) | → | F | | eqt(pending, excl) | → | F |
| eqt(pending, false) | → | F | | eqt(pending, lock) | → | F |
| eqt(pending, locker) | → | F | | eqt(pending, mcrlrecord) | → | F |
| eqt(pending, ok) | → | F | | eqt(pending, pending) | → | T |
| eqt(pending, release) | → | F | | eqt(pending, request) | → | F |
| eqt(pending, resource) | → | F | | eqt(pending, tag) | → | F |
| eqt(pending, true) | → | F | | eqt(pending, undefined) | → | F |
| eqt(pending, pid(N2)) | → | F | | eqt(pending, int(N2)) | → | F |
| eqt(pending, cons(H2, T2)) | → | F | | eqt(pending, tuple(H2, T2)) | → | F |
| eqt(pending, tuplenil(H2)) | → | F | | eqt(release, nil) | → | F |
| eqt(release, a) | → | F | | eqt(release, excl) | → | F |
| eqt(release, false) | → | F | | eqt(release, lock) | → | F |
| eqt(release, locker) | → | F | | eqt(release, mcrlrecord) | → | F |
| eqt(release, ok) | → | F | | eqt(request, mcrlrecord) | → | F |
| eqt(request, ok) | → | F | | eqt(request, pending) | → | F |
| eqt(request, release) | → | F | | eqt(request, request) | → | T |
| eqt(request, resource) | → | F | | eqt(request, tag) | → | F |
| eqt(request, true) | → | F | | eqt(request, undefined) | → | F |
| eqt(request, pid(N2)) | → | F | | eqt(request, int(N2)) | → | F |
| eqt(request, cons(H2, T2)) | → | F | | eqt(request, tuple(H2, T2)) | → | F |
| eqt(request, tuplenil(H2)) | → | F | | eqt(resource, nil) | → | F |
| eqt(resource, a) | → | F | | eqt(resource, excl) | → | F |
| eqt(resource, false) | → | F | | eqt(resource, lock) | → | F |
| eqt(resource, locker) | → | F | | eqt(resource, mcrlrecord) | → | F |
| eqt(resource, ok) | → | F | | eqt(resource, pending) | → | F |
| eqt(resource, release) | → | F | | eqt(resource, request) | → | F |
| eqt(resource, resource) | → | T | | eqt(resource, tag) | → | F |
| eqt(resource, true) | → | F | | eqt(resource, undefined) | → | F |
| eqt(resource, pid(N2)) | → | F | | eqt(resource, int(N2)) | → | F |
| eqt(resource, cons(H2, T2)) | → | F | | eqt(resource, tuple(H2, T2)) | → | F |
| eqt(resource, tuplenil(H2)) | → | F | | eqt(tag, nil) | → | F |
| eqt(tag, a) | → | F | | eqt(tag, excl) | → | F |
| eqt(tag, false) | → | F | | eqt(tag, lock) | → | F |
| eqt(tag, locker) | → | F | | eqt(tag, mcrlrecord) | → | F |
| eqt(tag, ok) | → | F | | eqt(tag, pending) | → | F |
| eqt(tag, release) | → | F | | eqt(tag, request) | → | F |
| eqt(tag, resource) | → | F | | eqt(tag, tag) | → | T |
| eqt(tag, true) | → | F | | eqt(tag, undefined) | → | F |
| eqt(tag, pid(N2)) | → | F | | eqt(tag, int(N2)) | → | F |
| eqt(tag, cons(H2, T2)) | → | F | | eqt(tag, tuple(H2, T2)) | → | F |
| eqt(tag, tuplenil(H2)) | → | F | | eqt(true, nil) | → | F |
| eqt(true, a) | → | F | | eqt(true, excl) | → | F |
| eqt(true, false) | → | F | | eqt(true, lock) | → | F |
| eqt(true, locker) | → | F | | eqt(true, mcrlrecord) | → | F |
| eqt(true, ok) | → | F | | eqt(true, pending) | → | F |
| eqt(true, release) | → | F | | eqt(true, request) | → | F |
| eqt(true, resource) | → | F | | eqt(true, tag) | → | F |
| eqt(true, true) | → | T | | eqt(true, undefined) | → | F |
| eqt(true, pid(N2)) | → | F | | eqt(true, int(N2)) | → | F |
| eqt(true, cons(H2, T2)) | → | F | | eqt(true, tuple(H2, T2)) | → | F |
| eqt(true, tuplenil(H2)) | → | F | | eqt(undefined, nil) | → | F |
| eqt(undefined, a) | → | F | | eqt(undefined, tuplenil(H2)) | → | F |
| eqt(pid(N1), nil) | → | F | | eqt(pid(N1), a) | → | F |
| eqt(pid(N1), excl) | → | F | | eqt(pid(N1), false) | → | F |
| eqt(pid(N1), lock) | → | F | | eqt(pid(N1), locker) | → | F |
| eqt(pid(N1), mcrlrecord) | → | F | | eqt(pid(N1), ok) | → | F |
| eqt(pid(N1), pending) | → | F | | eqt(pid(N1), release) | → | F |
| eqt(pid(N1), request) | → | F | | eqt(pid(N1), resource) | → | F |
| eqt(pid(N1), tag) | → | F | | eqt(pid(N1), true) | → | F |
| eqt(pid(N1), undefined) | → | F | | eqt(pid(N1), pid(N2)) | → | eqt(N1, N2) |
| eqt(pid(N1), int(N2)) | → | F | | eqt(pid(N1), cons(H2, T2)) | → | F |
| eqt(pid(N1), tuple(H2, T2)) | → | F | | eqt(pid(N1), tuplenil(H2)) | → | F |
| eqt(int(N1), nil) | → | F | | eqt(int(N1), a) | → | F |
| eqt(int(N1), excl) | → | F | | eqt(int(N1), false) | → | F |
| eqt(int(N1), lock) | → | F | | eqt(int(N1), locker) | → | F |
| eqt(int(N1), mcrlrecord) | → | F | | eqt(int(N1), ok) | → | F |
| eqt(int(N1), pending) | → | F | | eqt(int(N1), release) | → | F |
| eqt(int(N1), request) | → | F | | eqt(int(N1), resource) | → | F |
| eqt(int(N1), tag) | → | F | | eqt(int(N1), true) | → | F |
| eqt(int(N1), undefined) | → | F | | eqt(cons(H1, T1), resource) | → | F |
| eqt(cons(H1, T1), tag) | → | F | | eqt(cons(H1, T1), true) | → | F |
| eqt(cons(H1, T1), undefined) | → | F | | eqt(cons(H1, T1), pid(N2)) | → | F |
| eqt(cons(H1, T1), int(N2)) | → | F | | eqt(cons(H1, T1), cons(H2, T2)) | → | and(eqt(H1, H2), eqt(T1, T2)) |
| eqt(cons(H1, T1), tuple(H2, T2)) | → | F | | eqt(cons(H1, T1), tuplenil(H2)) | → | F |
| eqt(tuple(H1, T1), nil) | → | F | | eqt(tuple(H1, T1), a) | → | F |
| eqt(tuple(H1, T1), excl) | → | F | | eqt(tuple(H1, T1), false) | → | F |
| eqt(tuple(H1, T1), lock) | → | F | | eqt(tuple(H1, T1), locker) | → | F |
| eqt(tuple(H1, T1), mcrlrecord) | → | F | | eqt(tuple(H1, T1), ok) | → | F |
| eqt(tuple(H1, T1), pending) | → | F | | eqt(tuple(H1, T1), release) | → | F |
| eqt(tuple(H1, T1), request) | → | F | | eqt(tuple(H1, T1), resource) | → | F |
| eqt(tuple(H1, T1), tag) | → | F | | eqt(tuple(H1, T1), true) | → | F |
| eqt(tuple(H1, T1), undefined) | → | F | | eqt(tuple(H1, T1), pid(N2)) | → | F |
| eqt(tuple(H1, T1), int(N2)) | → | F | | eqt(tuple(H1, T1), cons(H2, T2)) | → | F |
| eqt(tuple(H1, T1), tuple(H2, T2)) | → | and(eqt(H1, H2), eqt(T1, T2)) | | eqt(tuple(H1, T1), tuplenil(H2)) | → | F |
| eqt(tuplenil(H1), nil) | → | F | | eqt(tuplenil(H1), a) | → | F |
| eqt(tuplenil(H1), excl) | → | F | | eqt(tuplenil(H1), false) | → | F |
| eqt(tuplenil(H1), lock) | → | F | | eqt(tuplenil(H1), locker) | → | F |
| eqt(tuplenil(H1), mcrlrecord) | → | F | | eqt(tuplenil(H1), ok) | → | F |
| eqt(tuplenil(H1), pending) | → | F | | eqt(tuplenil(H1), release) | → | F |
| eqt(tuplenil(H1), request) | → | F | | eqt(tuplenil(H1), resource) | → | F |
| eqt(tuplenil(H1), tag) | → | F | | eqt(tuplenil(H1), true) | → | F |
| eqt(tuplenil(H1), undefined) | → | F | | eqt(tuplenil(H1), pid(N2)) | → | F |
| eqt(tuplenil(H1), int(N2)) | → | F | | eqt(tuplenil(H1), cons(H2, T2)) | → | F |
| eqt(tuplenil(H1), tuple(H2, T2)) | → | F | | eqt(tuplenil(H1), tuplenil(H2)) | → | eqt(H1, H2) |
| element(int(s(0)), tuplenil(T1)) | → | T1 | | element(int(s(0)), tuple(T1, T2)) | → | T1 |
| element(int(s(s(N1))), tuple(T1, T2)) | → | element(int(s(N1)), T2) | | record_new(lock) | → | tuple(mcrlrecord, tuple(lock, tuple(undefined, tuple(nil, tuplenil(nil))))) |
| record_extract(tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2))))), lock, resource) | → | tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2))))) | | record_update(tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2))))), lock, pending, NewF) | → | tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(NewF))))) |
| record_updates(Record, Name, nil) | → | Record | | record_updates(Record, Name, cons(tuple(Field, tuplenil(NewF)), Fields)) | → | record_updates(record_update(Record, Name, Field, NewF), Name, Fields) |
| locker2_map_promote_pending(nil, Pending) | → | nil | | locker2_map_promote_pending(cons(Lock, Locks), Pending) | → | cons(locker2_promote_pending(Lock, Pending), locker2_map_promote_pending(Locks, Pending)) |
| locker2_map_claim_lock(nil, Resources, Client) | → | nil | | locker2_map_claim_lock(cons(Lock, Locks), Resources, Client) | → | cons(locker2_claim_lock(Lock, Resources, Client), locker2_map_claim_lock(Locks, Resources, Client)) |
| locker2_map_add_pending(nil, Resources, Client) | → | nil | | locker2_promote_pending(Lock, Client) | → | case0(Client, Lock, record_extract(Lock, lock, pending)) |
| case0(Client, Lock, cons(Client, Pendings)) | → | record_updates(Lock, lock, cons(tuple(excl, tuplenil(Client)), cons(tuple(pending, tuplenil(Pendings)), nil))) | | case0(Client, Lock, MCRLFree0) | → | Lock |
| locker2_remove_pending(Lock, Client) | → | record_updates(Lock, lock, cons(tuple(pending, tuplenil(subtract(record_extract(Lock, lock, pending), cons(Client, nil)))), nil)) | | locker2_add_pending(Lock, Resources, Client) | → | case1(Client, Resources, Lock, member(record_extract(Lock, lock, resource), Resources)) |
| case1(Client, Resources, Lock, true) | → | record_updates(Lock, lock, cons(tuple(pending, tuplenil(append(record_extract(Lock, lock, pending), cons(Client, nil)))), nil)) | | case1(Client, Resources, Lock, false) | → | Lock |
| locker2_release_lock(Lock, Client) | → | case2(Client, Lock, gen_modtageq(Client, record_extract(Lock, lock, excl))) | | case2(Client, Lock, true) | → | record_updates(Lock, lock, cons(tuple(excllock, excl), nil)) |
| case4(Client, Lock, MCRLFree1) | → | false | | locker2_obtainables(nil, Client) | → | true |
| locker2_obtainables(cons(Lock, Locks), Client) | → | case5(Client, Locks, Lock, member(Client, record_extract(Lock, lock, pending))) | | case5(Client, Locks, Lock, true) | → | andt(locker2_obtainable(Lock, Client), locker2_obtainables(Locks, Client)) |
| case5(Client, Locks, Lock, false) | → | locker2_obtainables(Locks, Client) | | locker2_check_available(Resource, nil) | → | false |
| locker2_check_available(Resource, cons(Lock, Locks)) | → | case6(Locks, Lock, Resource, equal(Resource, record_extract(Lock, lock, resource))) | | case6(Locks, Lock, Resource, true) | → | andt(equal(record_extract(Lock, lock, excl), nil), equal(record_extract(Lock, lock, pending), nil)) |
| case6(Locks, Lock, Resource, false) | → | locker2_check_available(Resource, Locks) | | locker2_check_availables(nil, Locks) | → | true |
| locker2_check_availables(cons(Resource, Resources), Locks) | → | andt(locker2_check_available(Resource, Locks), locker2_check_availables(Resources, Locks)) | | locker2_adduniq(nil, List) | → | List |
| append(cons(Head, Tail), List) | → | cons(Head, append(Tail, List)) | | subtract(List, nil) | → | List |
| subtract(List, cons(Head, Tail)) | → | subtract(delete(Head, List), Tail) | | delete(E, nil) | → | nil |
| delete(E, cons(Head, Tail)) | → | case8(Tail, Head, E, equal(E, Head)) | | case8(Tail, Head, E, true) | → | Tail |
| case8(Tail, Head, E, false) | → | cons(Head, delete(E, Tail)) | | gen_tag(Pid) | → | tuple(Pid, tuplenil(tag)) |
| gen_modtageq(Client1, Client2) | → | equal(Client1, Client2) | | member(E, nil) | → | false |
| member(E, cons(Head, Tail)) | → | case9(Tail, Head, E, equal(E, Head)) | | case9(Tail, Head, E, true) | → | true |
| case9(Tail, Head, E, false) | → | member(E, Tail) | | eqs(empty, empty) | → | T |
| eqs(empty, stack(E2, S2)) | → | F | | eqs(stack(E1, S1), empty) | → | F |
| eqs(stack(E1, S1), stack(E2, S2)) | → | and(eqt(E1, E2), eqs(S1, S2)) | | pushs(E1, S1) | → | stack(E1, S1) |
| pops(stack(E1, S1)) | → | S1 | | tops(stack(E1, S1)) | → | E1 |
| istops(E1, empty) | → | F | | istops(E1, stack(E2, S1)) | → | eqt(E1, E2) |
| eqc(nocalls, nocalls) | → | T | | eqc(nocalls, calls(E2, S2, CS2)) | → | F |
| eqc(calls(E1, S1, CS1), nocalls) | → | F | | eqc(calls(E1, S1, CS1), calls(E2, S2, CS2)) | → | and(eqt(E1, E2), and(eqs(S1, S2), eqc(CS1, CS2))) |
| push(E1, E2, nocalls) | → | calls(E1, stack(E2, empty), nocalls) | | push(E1, E2, calls(E3, S1, CS1)) | → | push1(E1, E2, E3, S1, CS1, eqt(E1, E3)) |
| push1(E1, E2, E3, S1, CS1, T) | → | calls(E3, pushs(E2, S1), CS1) |
Original Signature
Termination of terms over the following signature is verified: tuplenil, record_new, tuple, tag, gen_tag, imp, locker2_map_promote_pending, pops, locker2_check_availables, mcrlrecord, pending, request, empty, false, ok, istops, locker2_add_pending, andt, case2, append, element, case1, case0, tops, push1, case6, case5, or, int, case4, record_extract, locker, case9, case8, locker2_map_add_pending, calls, eqc, and, not, 0, locker2_promote_pending, locker2_claim_lock, locker2_adduniq, stack, release, locker2_obtainables, F, locker2_remove_pending, push, T, gen_modtageq, record_update, undefined, if, record_updates, eqt, excllock, delete, eqs, cons, member, locker2_map_claim_lock, locker2_obtainable, a, pushs, resource, lock, true, locker2_release_lock, pid, equal, subtract, locker2_check_available, s, excl, nil, eq, nocalls
Strategy
Projection
The following projection was used:
Thus, the following dependency pairs are removed:
| record_updates#(Record, Name, cons(tuple(Field, tuplenil(NewF)), Fields)) | → | record_updates#(record_update(Record, Name, Field, NewF), Name, Fields) |
Problem 12: SubtermCriterion
Dependency Pair Problem
Dependency Pairs
| append#(cons(Head, Tail), List) | → | append#(Tail, List) |
Rewrite Rules
| or(T, T) | → | T | | or(F, T) | → | T |
| or(T, F) | → | T | | or(F, F) | → | F |
| and(T, B) | → | B | | and(B, T) | → | B |
| and(F, B) | → | F | | and(B, F) | → | F |
| imp(T, B) | → | B | | imp(F, B) | → | T |
| not(T) | → | F | | not(F) | → | T |
| if(T, B1, B2) | → | B1 | | if(F, B1, B2) | → | B2 |
| eq(T, T) | → | T | | eq(F, F) | → | T |
| eq(T, F) | → | F | | eq(F, T) | → | F |
| eqt(nil, undefined) | → | F | | eqt(nil, pid(N2)) | → | F |
| eqt(nil, int(N2)) | → | F | | eqt(nil, cons(H2, T2)) | → | F |
| eqt(nil, tuple(H2, T2)) | → | F | | eqt(nil, tuplenil(H2)) | → | F |
| eqt(a, nil) | → | F | | eqt(a, a) | → | T |
| eqt(a, excl) | → | F | | eqt(a, false) | → | F |
| eqt(a, lock) | → | F | | eqt(a, locker) | → | F |
| eqt(a, mcrlrecord) | → | F | | eqt(a, ok) | → | F |
| eqt(a, pending) | → | F | | eqt(a, release) | → | F |
| eqt(a, request) | → | F | | eqt(a, resource) | → | F |
| eqt(a, tag) | → | F | | eqt(a, true) | → | F |
| eqt(a, undefined) | → | F | | eqt(a, pid(N2)) | → | F |
| eqt(a, int(N2)) | → | F | | eqt(a, cons(H2, T2)) | → | F |
| eqt(a, tuple(H2, T2)) | → | F | | eqt(a, tuplenil(H2)) | → | F |
| eqt(excl, nil) | → | F | | eqt(excl, a) | → | F |
| eqt(excl, excl) | → | T | | eqt(excl, false) | → | F |
| eqt(excl, lock) | → | F | | eqt(excl, locker) | → | F |
| eqt(excl, mcrlrecord) | → | F | | eqt(excl, ok) | → | F |
| eqt(excl, pending) | → | F | | eqt(excl, release) | → | F |
| eqt(excl, request) | → | F | | eqt(excl, resource) | → | F |
| eqt(excl, tag) | → | F | | eqt(excl, true) | → | F |
| eqt(excl, undefined) | → | F | | eqt(excl, pid(N2)) | → | F |
| eqt(excl, eqt(false, int(N2))) | → | F | | eqt(false, cons(H2, T2)) | → | F |
| eqt(false, tuple(H2, T2)) | → | F | | eqt(false, tuplenil(H2)) | → | F |
| eqt(lock, nil) | → | F | | eqt(lock, a) | → | F |
| eqt(lock, excl) | → | F | | eqt(lock, false) | → | F |
| eqt(lock, lock) | → | T | | eqt(lock, locker) | → | F |
| eqt(lock, mcrlrecord) | → | F | | eqt(lock, ok) | → | F |
| eqt(lock, pending) | → | F | | eqt(lock, release) | → | F |
| eqt(lock, request) | → | F | | eqt(lock, resource) | → | F |
| eqt(lock, tag) | → | F | | eqt(lock, true) | → | F |
| eqt(lock, undefined) | → | F | | eqt(lock, pid(N2)) | → | F |
| eqt(lock, int(N2)) | → | F | | eqt(lock, cons(H2, T2)) | → | F |
| eqt(lock, tuple(H2, T2)) | → | F | | eqt(lock, tuplenil(H2)) | → | F |
| eqt(locker, nil) | → | F | | eqt(locker, a) | → | F |
| eqt(locker, excl) | → | F | | eqt(locker, false) | → | F |
| eqt(locker, lock) | → | F | | eqt(locker, locker) | → | T |
| eqt(locker, mcrlrecord) | → | F | | eqt(locker, ok) | → | F |
| eqt(locker, pending) | → | F | | eqt(locker, release) | → | F |
| eqt(locker, request) | → | F | | eqt(locker, resource) | → | F |
| eqt(locker, tag) | → | F | | eqt(locker, true) | → | F |
| eqt(locker, undefined) | → | F | | eqt(locker, pid(N2)) | → | F |
| eqt(locker, int(N2)) | → | F | | eqt(locker, cons(H2, T2)) | → | F |
| eqt(locker, tuple(H2, T2)) | → | F | | eqt(locker, tuplenil(H2)) | → | F |
| eqt(mcrlrecord, nil) | → | F | | eqt(mcrlrecord, a) | → | F |
| eqt(mcrlrecord, excl) | → | F | | eqt(mcrlrecord, false) | → | F |
| eqt(mcrlrecord, lock) | → | F | | eqt(mcrlrecord, locker) | → | F |
| eqt(mcrlrecord, mcrlrecord) | → | T | | eqt(mcrlrecord, ok) | → | F |
| eqt(mcrlrecord, pending) | → | F | | eqt(mcrlrecord, release) | → | F |
| eqt(mcrlrecord, request) | → | F | | eqt(mcrlrecord, resource) | → | F |
| eqt(ok, resource) | → | F | | eqt(ok, tag) | → | F |
| eqt(ok, true) | → | F | | eqt(ok, undefined) | → | F |
| eqt(ok, pid(N2)) | → | F | | eqt(ok, int(N2)) | → | F |
| eqt(ok, cons(H2, T2)) | → | F | | eqt(ok, tuple(H2, T2)) | → | F |
| eqt(ok, tuplenil(H2)) | → | F | | eqt(pending, nil) | → | F |
| eqt(pending, a) | → | F | | eqt(pending, excl) | → | F |
| eqt(pending, false) | → | F | | eqt(pending, lock) | → | F |
| eqt(pending, locker) | → | F | | eqt(pending, mcrlrecord) | → | F |
| eqt(pending, ok) | → | F | | eqt(pending, pending) | → | T |
| eqt(pending, release) | → | F | | eqt(pending, request) | → | F |
| eqt(pending, resource) | → | F | | eqt(pending, tag) | → | F |
| eqt(pending, true) | → | F | | eqt(pending, undefined) | → | F |
| eqt(pending, pid(N2)) | → | F | | eqt(pending, int(N2)) | → | F |
| eqt(pending, cons(H2, T2)) | → | F | | eqt(pending, tuple(H2, T2)) | → | F |
| eqt(pending, tuplenil(H2)) | → | F | | eqt(release, nil) | → | F |
| eqt(release, a) | → | F | | eqt(release, excl) | → | F |
| eqt(release, false) | → | F | | eqt(release, lock) | → | F |
| eqt(release, locker) | → | F | | eqt(release, mcrlrecord) | → | F |
| eqt(release, ok) | → | F | | eqt(request, mcrlrecord) | → | F |
| eqt(request, ok) | → | F | | eqt(request, pending) | → | F |
| eqt(request, release) | → | F | | eqt(request, request) | → | T |
| eqt(request, resource) | → | F | | eqt(request, tag) | → | F |
| eqt(request, true) | → | F | | eqt(request, undefined) | → | F |
| eqt(request, pid(N2)) | → | F | | eqt(request, int(N2)) | → | F |
| eqt(request, cons(H2, T2)) | → | F | | eqt(request, tuple(H2, T2)) | → | F |
| eqt(request, tuplenil(H2)) | → | F | | eqt(resource, nil) | → | F |
| eqt(resource, a) | → | F | | eqt(resource, excl) | → | F |
| eqt(resource, false) | → | F | | eqt(resource, lock) | → | F |
| eqt(resource, locker) | → | F | | eqt(resource, mcrlrecord) | → | F |
| eqt(resource, ok) | → | F | | eqt(resource, pending) | → | F |
| eqt(resource, release) | → | F | | eqt(resource, request) | → | F |
| eqt(resource, resource) | → | T | | eqt(resource, tag) | → | F |
| eqt(resource, true) | → | F | | eqt(resource, undefined) | → | F |
| eqt(resource, pid(N2)) | → | F | | eqt(resource, int(N2)) | → | F |
| eqt(resource, cons(H2, T2)) | → | F | | eqt(resource, tuple(H2, T2)) | → | F |
| eqt(resource, tuplenil(H2)) | → | F | | eqt(tag, nil) | → | F |
| eqt(tag, a) | → | F | | eqt(tag, excl) | → | F |
| eqt(tag, false) | → | F | | eqt(tag, lock) | → | F |
| eqt(tag, locker) | → | F | | eqt(tag, mcrlrecord) | → | F |
| eqt(tag, ok) | → | F | | eqt(tag, pending) | → | F |
| eqt(tag, release) | → | F | | eqt(tag, request) | → | F |
| eqt(tag, resource) | → | F | | eqt(tag, tag) | → | T |
| eqt(tag, true) | → | F | | eqt(tag, undefined) | → | F |
| eqt(tag, pid(N2)) | → | F | | eqt(tag, int(N2)) | → | F |
| eqt(tag, cons(H2, T2)) | → | F | | eqt(tag, tuple(H2, T2)) | → | F |
| eqt(tag, tuplenil(H2)) | → | F | | eqt(true, nil) | → | F |
| eqt(true, a) | → | F | | eqt(true, excl) | → | F |
| eqt(true, false) | → | F | | eqt(true, lock) | → | F |
| eqt(true, locker) | → | F | | eqt(true, mcrlrecord) | → | F |
| eqt(true, ok) | → | F | | eqt(true, pending) | → | F |
| eqt(true, release) | → | F | | eqt(true, request) | → | F |
| eqt(true, resource) | → | F | | eqt(true, tag) | → | F |
| eqt(true, true) | → | T | | eqt(true, undefined) | → | F |
| eqt(true, pid(N2)) | → | F | | eqt(true, int(N2)) | → | F |
| eqt(true, cons(H2, T2)) | → | F | | eqt(true, tuple(H2, T2)) | → | F |
| eqt(true, tuplenil(H2)) | → | F | | eqt(undefined, nil) | → | F |
| eqt(undefined, a) | → | F | | eqt(undefined, tuplenil(H2)) | → | F |
| eqt(pid(N1), nil) | → | F | | eqt(pid(N1), a) | → | F |
| eqt(pid(N1), excl) | → | F | | eqt(pid(N1), false) | → | F |
| eqt(pid(N1), lock) | → | F | | eqt(pid(N1), locker) | → | F |
| eqt(pid(N1), mcrlrecord) | → | F | | eqt(pid(N1), ok) | → | F |
| eqt(pid(N1), pending) | → | F | | eqt(pid(N1), release) | → | F |
| eqt(pid(N1), request) | → | F | | eqt(pid(N1), resource) | → | F |
| eqt(pid(N1), tag) | → | F | | eqt(pid(N1), true) | → | F |
| eqt(pid(N1), undefined) | → | F | | eqt(pid(N1), pid(N2)) | → | eqt(N1, N2) |
| eqt(pid(N1), int(N2)) | → | F | | eqt(pid(N1), cons(H2, T2)) | → | F |
| eqt(pid(N1), tuple(H2, T2)) | → | F | | eqt(pid(N1), tuplenil(H2)) | → | F |
| eqt(int(N1), nil) | → | F | | eqt(int(N1), a) | → | F |
| eqt(int(N1), excl) | → | F | | eqt(int(N1), false) | → | F |
| eqt(int(N1), lock) | → | F | | eqt(int(N1), locker) | → | F |
| eqt(int(N1), mcrlrecord) | → | F | | eqt(int(N1), ok) | → | F |
| eqt(int(N1), pending) | → | F | | eqt(int(N1), release) | → | F |
| eqt(int(N1), request) | → | F | | eqt(int(N1), resource) | → | F |
| eqt(int(N1), tag) | → | F | | eqt(int(N1), true) | → | F |
| eqt(int(N1), undefined) | → | F | | eqt(cons(H1, T1), resource) | → | F |
| eqt(cons(H1, T1), tag) | → | F | | eqt(cons(H1, T1), true) | → | F |
| eqt(cons(H1, T1), undefined) | → | F | | eqt(cons(H1, T1), pid(N2)) | → | F |
| eqt(cons(H1, T1), int(N2)) | → | F | | eqt(cons(H1, T1), cons(H2, T2)) | → | and(eqt(H1, H2), eqt(T1, T2)) |
| eqt(cons(H1, T1), tuple(H2, T2)) | → | F | | eqt(cons(H1, T1), tuplenil(H2)) | → | F |
| eqt(tuple(H1, T1), nil) | → | F | | eqt(tuple(H1, T1), a) | → | F |
| eqt(tuple(H1, T1), excl) | → | F | | eqt(tuple(H1, T1), false) | → | F |
| eqt(tuple(H1, T1), lock) | → | F | | eqt(tuple(H1, T1), locker) | → | F |
| eqt(tuple(H1, T1), mcrlrecord) | → | F | | eqt(tuple(H1, T1), ok) | → | F |
| eqt(tuple(H1, T1), pending) | → | F | | eqt(tuple(H1, T1), release) | → | F |
| eqt(tuple(H1, T1), request) | → | F | | eqt(tuple(H1, T1), resource) | → | F |
| eqt(tuple(H1, T1), tag) | → | F | | eqt(tuple(H1, T1), true) | → | F |
| eqt(tuple(H1, T1), undefined) | → | F | | eqt(tuple(H1, T1), pid(N2)) | → | F |
| eqt(tuple(H1, T1), int(N2)) | → | F | | eqt(tuple(H1, T1), cons(H2, T2)) | → | F |
| eqt(tuple(H1, T1), tuple(H2, T2)) | → | and(eqt(H1, H2), eqt(T1, T2)) | | eqt(tuple(H1, T1), tuplenil(H2)) | → | F |
| eqt(tuplenil(H1), nil) | → | F | | eqt(tuplenil(H1), a) | → | F |
| eqt(tuplenil(H1), excl) | → | F | | eqt(tuplenil(H1), false) | → | F |
| eqt(tuplenil(H1), lock) | → | F | | eqt(tuplenil(H1), locker) | → | F |
| eqt(tuplenil(H1), mcrlrecord) | → | F | | eqt(tuplenil(H1), ok) | → | F |
| eqt(tuplenil(H1), pending) | → | F | | eqt(tuplenil(H1), release) | → | F |
| eqt(tuplenil(H1), request) | → | F | | eqt(tuplenil(H1), resource) | → | F |
| eqt(tuplenil(H1), tag) | → | F | | eqt(tuplenil(H1), true) | → | F |
| eqt(tuplenil(H1), undefined) | → | F | | eqt(tuplenil(H1), pid(N2)) | → | F |
| eqt(tuplenil(H1), int(N2)) | → | F | | eqt(tuplenil(H1), cons(H2, T2)) | → | F |
| eqt(tuplenil(H1), tuple(H2, T2)) | → | F | | eqt(tuplenil(H1), tuplenil(H2)) | → | eqt(H1, H2) |
| element(int(s(0)), tuplenil(T1)) | → | T1 | | element(int(s(0)), tuple(T1, T2)) | → | T1 |
| element(int(s(s(N1))), tuple(T1, T2)) | → | element(int(s(N1)), T2) | | record_new(lock) | → | tuple(mcrlrecord, tuple(lock, tuple(undefined, tuple(nil, tuplenil(nil))))) |
| record_extract(tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2))))), lock, resource) | → | tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2))))) | | record_update(tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(F2))))), lock, pending, NewF) | → | tuple(mcrlrecord, tuple(lock, tuple(F0, tuple(F1, tuplenil(NewF))))) |
| record_updates(Record, Name, nil) | → | Record | | record_updates(Record, Name, cons(tuple(Field, tuplenil(NewF)), Fields)) | → | record_updates(record_update(Record, Name, Field, NewF), Name, Fields) |
| locker2_map_promote_pending(nil, Pending) | → | nil | | locker2_map_promote_pending(cons(Lock, Locks), Pending) | → | cons(locker2_promote_pending(Lock, Pending), locker2_map_promote_pending(Locks, Pending)) |
| locker2_map_claim_lock(nil, Resources, Client) | → | nil | | locker2_map_claim_lock(cons(Lock, Locks), Resources, Client) | → | cons(locker2_claim_lock(Lock, Resources, Client), locker2_map_claim_lock(Locks, Resources, Client)) |
| locker2_map_add_pending(nil, Resources, Client) | → | nil | | locker2_promote_pending(Lock, Client) | → | case0(Client, Lock, record_extract(Lock, lock, pending)) |
| case0(Client, Lock, cons(Client, Pendings)) | → | record_updates(Lock, lock, cons(tuple(excl, tuplenil(Client)), cons(tuple(pending, tuplenil(Pendings)), nil))) | | case0(Client, Lock, MCRLFree0) | → | Lock |
| locker2_remove_pending(Lock, Client) | → | record_updates(Lock, lock, cons(tuple(pending, tuplenil(subtract(record_extract(Lock, lock, pending), cons(Client, nil)))), nil)) | | locker2_add_pending(Lock, Resources, Client) | → | case1(Client, Resources, Lock, member(record_extract(Lock, lock, resource), Resources)) |
| case1(Client, Resources, Lock, true) | → | record_updates(Lock, lock, cons(tuple(pending, tuplenil(append(record_extract(Lock, lock, pending), cons(Client, nil)))), nil)) | | case1(Client, Resources, Lock, false) | → | Lock |
| locker2_release_lock(Lock, Client) | → | case2(Client, Lock, gen_modtageq(Client, record_extract(Lock, lock, excl))) | | case2(Client, Lock, true) | → | record_updates(Lock, lock, cons(tuple(excllock, excl), nil)) |
| case4(Client, Lock, MCRLFree1) | → | false | | locker2_obtainables(nil, Client) | → | true |
| locker2_obtainables(cons(Lock, Locks), Client) | → | case5(Client, Locks, Lock, member(Client, record_extract(Lock, lock, pending))) | | case5(Client, Locks, Lock, true) | → | andt(locker2_obtainable(Lock, Client), locker2_obtainables(Locks, Client)) |
| case5(Client, Locks, Lock, false) | → | locker2_obtainables(Locks, Client) | | locker2_check_available(Resource, nil) | → | false |
| locker2_check_available(Resource, cons(Lock, Locks)) | → | case6(Locks, Lock, Resource, equal(Resource, record_extract(Lock, lock, resource))) | | case6(Locks, Lock, Resource, true) | → | andt(equal(record_extract(Lock, lock, excl), nil), equal(record_extract(Lock, lock, pending), nil)) |
| case6(Locks, Lock, Resource, false) | → | locker2_check_available(Resource, Locks) | | locker2_check_availables(nil, Locks) | → | true |
| locker2_check_availables(cons(Resource, Resources), Locks) | → | andt(locker2_check_available(Resource, Locks), locker2_check_availables(Resources, Locks)) | | locker2_adduniq(nil, List) | → | List |
| append(cons(Head, Tail), List) | → | cons(Head, append(Tail, List)) | | subtract(List, nil) | → | List |
| subtract(List, cons(Head, Tail)) | → | subtract(delete(Head, List), Tail) | | delete(E, nil) | → | nil |
| delete(E, cons(Head, Tail)) | → | case8(Tail, Head, E, equal(E, Head)) | | case8(Tail, Head, E, true) | → | Tail |
| case8(Tail, Head, E, false) | → | cons(Head, delete(E, Tail)) | | gen_tag(Pid) | → | tuple(Pid, tuplenil(tag)) |
| gen_modtageq(Client1, Client2) | → | equal(Client1, Client2) | | member(E, nil) | → | false |
| member(E, cons(Head, Tail)) | → | case9(Tail, Head, E, equal(E, Head)) | | case9(Tail, Head, E, true) | → | true |
| case9(Tail, Head, E, false) | → | member(E, Tail) | | eqs(empty, empty) | → | T |
| eqs(empty, stack(E2, S2)) | → | F | | eqs(stack(E1, S1), empty) | → | F |
| eqs(stack(E1, S1), stack(E2, S2)) | → | and(eqt(E1, E2), eqs(S1, S2)) | | pushs(E1, S1) | → | stack(E1, S1) |
| pops(stack(E1, S1)) | → | S1 | | tops(stack(E1, S1)) | → | E1 |
| istops(E1, empty) | → | F | | istops(E1, stack(E2, S1)) | → | eqt(E1, E2) |
| eqc(nocalls, nocalls) | → | T | | eqc(nocalls, calls(E2, S2, CS2)) | → | F |
| eqc(calls(E1, S1, CS1), nocalls) | → | F | | eqc(calls(E1, S1, CS1), calls(E2, S2, CS2)) | → | and(eqt(E1, E2), and(eqs(S1, S2), eqc(CS1, CS2))) |
| push(E1, E2, nocalls) | → | calls(E1, stack(E2, empty), nocalls) | | push(E1, E2, calls(E3, S1, CS1)) | → | push1(E1, E2, E3, S1, CS1, eqt(E1, E3)) |
| push1(E1, E2, E3, S1, CS1, T) | → | calls(E3, pushs(E2, S1), CS1) |
Original Signature
Termination of terms over the following signature is verified: tuplenil, record_new, tuple, tag, gen_tag, imp, locker2_map_promote_pending, pops, locker2_check_availables, mcrlrecord, pending, request, empty, false, ok, istops, locker2_add_pending, andt, case2, append, element, case1, case0, tops, push1, case6, case5, or, int, case4, record_extract, locker, case9, case8, locker2_map_add_pending, calls, eqc, and, not, 0, locker2_promote_pending, locker2_claim_lock, locker2_adduniq, stack, release, locker2_obtainables, F, locker2_remove_pending, push, T, gen_modtageq, record_update, undefined, if, record_updates, eqt, excllock, delete, eqs, cons, member, locker2_map_claim_lock, locker2_obtainable, a, pushs, resource, lock, true, locker2_release_lock, pid, equal, subtract, locker2_check_available, s, excl, nil, eq, nocalls
Strategy
Projection
The following projection was used:
Thus, the following dependency pairs are removed:
| append#(cons(Head, Tail), List) | → | append#(Tail, List) |