The TRS could not be proven terminating. The proof attempt took 60017 ms.
Problem 1 remains open; application of the following processors failed [DependencyGraph (timeout)].
| active#(U31(tt, V)) | → | U32#(isQid(V)) | active#(isPalListKind(__(V1, V2))) | → | and#(isPalListKind(V1), isPalListKind(V2)) | |
| active#(__(__(X, Y), Z)) | → | __#(X, __(Y, Z)) | active#(U12(X)) | → | active#(X) | |
| U11#(mark(X1), X2) | → | U11#(X1, X2) | proper#(U62(X)) | → | proper#(X) | |
| top#(mark(X)) | → | proper#(X) | U43#(ok(X)) | → | U43#(X) | |
| __#(mark(X1), X2) | → | __#(X1, X2) | proper#(U71(X1, X2)) | → | U71#(proper(X1), proper(X2)) | |
| active#(U32(X)) | → | active#(X) | active#(U61(X1, X2)) | → | active#(X1) | |
| proper#(U12(X)) | → | U12#(proper(X)) | and#(mark(X1), X2) | → | and#(X1, X2) | |
| U42#(mark(X1), X2) | → | U42#(X1, X2) | active#(U42(X1, X2)) | → | U42#(active(X1), X2) | |
| U53#(mark(X)) | → | U53#(X) | proper#(isNePal(X)) | → | isNePal#(proper(X)) | |
| isQid#(ok(X)) | → | isQid#(X) | proper#(U23(X)) | → | U23#(proper(X)) | |
| proper#(U52(X1, X2)) | → | proper#(X1) | proper#(U21(X1, X2, X3)) | → | proper#(X3) | |
| active#(U41(X1, X2, X3)) | → | U41#(active(X1), X2, X3) | active#(isPalListKind(__(V1, V2))) | → | isPalListKind#(V1) | |
| U32#(mark(X)) | → | U32#(X) | active#(U52(X1, X2)) | → | active#(X1) | |
| active#(and(X1, X2)) | → | and#(active(X1), X2) | active#(U53(X)) | → | active#(X) | |
| proper#(U41(X1, X2, X3)) | → | proper#(X1) | U52#(ok(X1), ok(X2)) | → | U52#(X1, X2) | |
| active#(U31(X1, X2)) | → | active#(X1) | active#(U22(X1, X2)) | → | active#(X1) | |
| proper#(isList(X)) | → | isList#(proper(X)) | proper#(U22(X1, X2)) | → | U22#(proper(X1), proper(X2)) | |
| U41#(ok(X1), ok(X2), ok(X3)) | → | U41#(X1, X2, X3) | __#(ok(X1), ok(X2)) | → | __#(X1, X2) | |
| __#(X1, mark(X2)) | → | __#(X1, X2) | active#(U11(X1, X2)) | → | U11#(active(X1), X2) | |
| proper#(U42(X1, X2)) | → | U42#(proper(X1), proper(X2)) | proper#(U21(X1, X2, X3)) | → | U21#(proper(X1), proper(X2), proper(X3)) | |
| active#(isPal(V)) | → | U71#(isPalListKind(V), V) | U22#(ok(X1), ok(X2)) | → | U22#(X1, X2) | |
| active#(U51(X1, X2, X3)) | → | U51#(active(X1), X2, X3) | active#(isNePal(__(I, __(P, I)))) | → | and#(and(isQid(I), isPalListKind(I)), and(isPal(P), isPalListKind(P))) | |
| active#(U41(tt, V1, V2)) | → | U42#(isList(V1), V2) | active#(isNePal(__(I, __(P, I)))) | → | and#(isPal(P), isPalListKind(P)) | |
| proper#(U31(X1, X2)) | → | U31#(proper(X1), proper(X2)) | proper#(U21(X1, X2, X3)) | → | proper#(X2) | |
| U31#(ok(X1), ok(X2)) | → | U31#(X1, X2) | active#(isNeList(__(V1, V2))) | → | isPalListKind#(V2) | |
| U52#(mark(X1), X2) | → | U52#(X1, X2) | active#(U22(X1, X2)) | → | U22#(active(X1), X2) | |
| isPal#(ok(X)) | → | isPal#(X) | active#(U51(tt, V1, V2)) | → | U52#(isNeList(V1), V2) | |
| proper#(isList(X)) | → | proper#(X) | proper#(U11(X1, X2)) | → | U11#(proper(X1), proper(X2)) | |
| proper#(and(X1, X2)) | → | and#(proper(X1), proper(X2)) | U71#(ok(X1), ok(X2)) | → | U71#(X1, X2) | |
| U12#(mark(X)) | → | U12#(X) | proper#(U71(X1, X2)) | → | proper#(X2) | |
| active#(isNeList(__(V1, V2))) | → | and#(isPalListKind(V1), isPalListKind(V2)) | proper#(and(X1, X2)) | → | proper#(X2) | |
| proper#(U61(X1, X2)) | → | proper#(X2) | U61#(mark(X1), X2) | → | U61#(X1, X2) | |
| active#(isNeList(__(V1, V2))) | → | U51#(and(isPalListKind(V1), isPalListKind(V2)), V1, V2) | proper#(U41(X1, X2, X3)) | → | U41#(proper(X1), proper(X2), proper(X3)) | |
| proper#(U43(X)) | → | proper#(X) | U61#(ok(X1), ok(X2)) | → | U61#(X1, X2) | |
| active#(U51(X1, X2, X3)) | → | active#(X1) | active#(U21(tt, V1, V2)) | → | isList#(V1) | |
| active#(U72(X)) | → | U72#(active(X)) | active#(U21(X1, X2, X3)) | → | active#(X1) | |
| proper#(isQid(X)) | → | proper#(X) | proper#(U72(X)) | → | U72#(proper(X)) | |
| active#(U11(tt, V)) | → | isNeList#(V) | proper#(isPal(X)) | → | isPal#(proper(X)) | |
| active#(U21(tt, V1, V2)) | → | U22#(isList(V1), V2) | proper#(U31(X1, X2)) | → | proper#(X2) | |
| and#(ok(X1), ok(X2)) | → | and#(X1, X2) | active#(isNeList(__(V1, V2))) | → | isPalListKind#(V1) | |
| active#(U52(tt, V2)) | → | isList#(V2) | proper#(U32(X)) | → | proper#(X) | |
| active#(U12(X)) | → | U12#(active(X)) | active#(__(X1, X2)) | → | __#(X1, active(X2)) | |
| active#(U71(X1, X2)) | → | active#(X1) | U43#(mark(X)) | → | U43#(X) | |
| active#(__(X1, X2)) | → | active#(X1) | active#(U42(tt, V2)) | → | U43#(isNeList(V2)) | |
| active#(isNeList(__(V1, V2))) | → | U41#(and(isPalListKind(V1), isPalListKind(V2)), V1, V2) | proper#(isPalListKind(X)) | → | isPalListKind#(proper(X)) | |
| proper#(isNeList(X)) | → | isNeList#(proper(X)) | U12#(ok(X)) | → | U12#(X) | |
| proper#(U11(X1, X2)) | → | proper#(X1) | U21#(ok(X1), ok(X2), ok(X3)) | → | U21#(X1, X2, X3) | |
| proper#(U41(X1, X2, X3)) | → | proper#(X2) | proper#(U11(X1, X2)) | → | proper#(X2) | |
| active#(isList(V)) | → | isPalListKind#(V) | active#(U51(tt, V1, V2)) | → | isNeList#(V1) | |
| proper#(U23(X)) | → | proper#(X) | active#(__(X1, X2)) | → | __#(active(X1), X2) | |
| active#(isNePal(__(I, __(P, I)))) | → | and#(isQid(I), isPalListKind(I)) | active#(U43(X)) | → | U43#(active(X)) | |
| U21#(mark(X1), X2, X3) | → | U21#(X1, X2, X3) | active#(U62(X)) | → | active#(X) | |
| active#(U21(X1, X2, X3)) | → | U21#(active(X1), X2, X3) | active#(U41(X1, X2, X3)) | → | active#(X1) | |
| proper#(U51(X1, X2, X3)) | → | proper#(X1) | proper#(U32(X)) | → | U32#(proper(X)) | |
| active#(U71(tt, V)) | → | isNePal#(V) | active#(U53(X)) | → | U53#(active(X)) | |
| proper#(U62(X)) | → | U62#(proper(X)) | isPalListKind#(ok(X)) | → | isPalListKind#(X) | |
| proper#(U51(X1, X2, X3)) | → | proper#(X2) | U51#(ok(X1), ok(X2), ok(X3)) | → | U51#(X1, X2, X3) | |
| U72#(ok(X)) | → | U72#(X) | U22#(mark(X1), X2) | → | U22#(X1, X2) | |
| active#(isNePal(__(I, __(P, I)))) | → | isPalListKind#(P) | active#(U52(X1, X2)) | → | U52#(active(X1), X2) | |
| active#(isList(V)) | → | U11#(isPalListKind(V), V) | top#(ok(X)) | → | active#(X) | |
| active#(isPalListKind(__(V1, V2))) | → | isPalListKind#(V2) | proper#(U42(X1, X2)) | → | proper#(X1) | |
| active#(U11(tt, V)) | → | U12#(isNeList(V)) | active#(isList(__(V1, V2))) | → | isPalListKind#(V2) | |
| active#(__(X1, X2)) | → | active#(X2) | U62#(mark(X)) | → | U62#(X) | |
| proper#(U21(X1, X2, X3)) | → | proper#(X1) | isList#(ok(X)) | → | isList#(X) | |
| U71#(mark(X1), X2) | → | U71#(X1, X2) | proper#(U72(X)) | → | proper#(X) | |
| isNeList#(ok(X)) | → | isNeList#(X) | U51#(mark(X1), X2, X3) | → | U51#(X1, X2, X3) | |
| proper#(U12(X)) | → | proper#(X) | active#(__(__(X, Y), Z)) | → | __#(Y, Z) | |
| active#(isNePal(__(I, __(P, I)))) | → | isPalListKind#(I) | active#(U31(tt, V)) | → | isQid#(V) | |
| active#(U23(X)) | → | active#(X) | active#(isNeList(V)) | → | U31#(isPalListKind(V), V) | |
| active#(isNePal(V)) | → | U61#(isPalListKind(V), V) | active#(U41(tt, V1, V2)) | → | isList#(V1) | |
| active#(isNePal(V)) | → | isPalListKind#(V) | active#(U72(X)) | → | active#(X) | |
| top#(ok(X)) | → | top#(active(X)) | proper#(U42(X1, X2)) | → | proper#(X2) | |
| proper#(U31(X1, X2)) | → | proper#(X1) | U23#(mark(X)) | → | U23#(X) | |
| U11#(ok(X1), ok(X2)) | → | U11#(X1, X2) | U32#(ok(X)) | → | U32#(X) | |
| proper#(U52(X1, X2)) | → | U52#(proper(X1), proper(X2)) | active#(U61(X1, X2)) | → | U61#(active(X1), X2) | |
| proper#(isPal(X)) | → | proper#(X) | active#(U11(X1, X2)) | → | active#(X1) | |
| active#(U23(X)) | → | U23#(active(X)) | active#(U62(X)) | → | U62#(active(X)) | |
| proper#(__(X1, X2)) | → | proper#(X1) | top#(mark(X)) | → | top#(proper(X)) | |
| active#(U52(tt, V2)) | → | U53#(isList(V2)) | active#(U22(tt, V2)) | → | U23#(isList(V2)) | |
| proper#(isNePal(X)) | → | proper#(X) | active#(U71(tt, V)) | → | U72#(isNePal(V)) | |
| proper#(isNeList(X)) | → | proper#(X) | proper#(U22(X1, X2)) | → | proper#(X2) | |
| U62#(ok(X)) | → | U62#(X) | isNePal#(ok(X)) | → | isNePal#(X) | |
| proper#(isPalListKind(X)) | → | proper#(X) | U72#(mark(X)) | → | U72#(X) | |
| active#(isNeList(V)) | → | isPalListKind#(V) | proper#(U43(X)) | → | U43#(proper(X)) | |
| proper#(U51(X1, X2, X3)) | → | U51#(proper(X1), proper(X2), proper(X3)) | proper#(U61(X1, X2)) | → | U61#(proper(X1), proper(X2)) | |
| active#(U71(X1, X2)) | → | U71#(active(X1), X2) | proper#(U53(X)) | → | U53#(proper(X)) | |
| proper#(U41(X1, X2, X3)) | → | proper#(X3) | active#(U42(X1, X2)) | → | active#(X1) | |
| active#(isPal(V)) | → | isPalListKind#(V) | active#(U43(X)) | → | active#(X) | |
| proper#(and(X1, X2)) | → | proper#(X1) | U53#(ok(X)) | → | U53#(X) | |
| proper#(U22(X1, X2)) | → | proper#(X1) | proper#(__(X1, X2)) | → | __#(proper(X1), proper(X2)) | |
| active#(U31(X1, X2)) | → | U31#(active(X1), X2) | active#(isList(__(V1, V2))) | → | and#(isPalListKind(V1), isPalListKind(V2)) | |
| active#(isList(__(V1, V2))) | → | isPalListKind#(V1) | proper#(U71(X1, X2)) | → | proper#(X1) | |
| U41#(mark(X1), X2, X3) | → | U41#(X1, X2, X3) | proper#(U51(X1, X2, X3)) | → | proper#(X3) | |
| active#(U61(tt, V)) | → | isQid#(V) | U23#(ok(X)) | → | U23#(X) | |
| active#(isNePal(__(I, __(P, I)))) | → | isPal#(P) | proper#(isQid(X)) | → | isQid#(proper(X)) | |
| proper#(U53(X)) | → | proper#(X) | active#(U32(X)) | → | U32#(active(X)) | |
| U42#(ok(X1), ok(X2)) | → | U42#(X1, X2) | active#(U61(tt, V)) | → | U62#(isQid(V)) | |
| active#(isNePal(__(I, __(P, I)))) | → | isQid#(I) | proper#(__(X1, X2)) | → | proper#(X2) | |
| active#(U22(tt, V2)) | → | isList#(V2) | U31#(mark(X1), X2) | → | U31#(X1, X2) | |
| proper#(U61(X1, X2)) | → | proper#(X1) | proper#(U52(X1, X2)) | → | proper#(X2) | |
| active#(isList(__(V1, V2))) | → | U21#(and(isPalListKind(V1), isPalListKind(V2)), V1, V2) | active#(and(X1, X2)) | → | active#(X1) | |
| active#(U42(tt, V2)) | → | isNeList#(V2) |
| active(__(__(X, Y), Z)) | → | mark(__(X, __(Y, Z))) | active(__(X, nil)) | → | mark(X) | |
| active(__(nil, X)) | → | mark(X) | active(U11(tt, V)) | → | mark(U12(isNeList(V))) | |
| active(U12(tt)) | → | mark(tt) | active(U21(tt, V1, V2)) | → | mark(U22(isList(V1), V2)) | |
| active(U22(tt, V2)) | → | mark(U23(isList(V2))) | active(U23(tt)) | → | mark(tt) | |
| active(U31(tt, V)) | → | mark(U32(isQid(V))) | active(U32(tt)) | → | mark(tt) | |
| active(U41(tt, V1, V2)) | → | mark(U42(isList(V1), V2)) | active(U42(tt, V2)) | → | mark(U43(isNeList(V2))) | |
| active(U43(tt)) | → | mark(tt) | active(U51(tt, V1, V2)) | → | mark(U52(isNeList(V1), V2)) | |
| active(U52(tt, V2)) | → | mark(U53(isList(V2))) | active(U53(tt)) | → | mark(tt) | |
| active(U61(tt, V)) | → | mark(U62(isQid(V))) | active(U62(tt)) | → | mark(tt) | |
| active(U71(tt, V)) | → | mark(U72(isNePal(V))) | active(U72(tt)) | → | mark(tt) | |
| active(and(tt, X)) | → | mark(X) | active(isList(V)) | → | mark(U11(isPalListKind(V), V)) | |
| active(isList(nil)) | → | mark(tt) | active(isList(__(V1, V2))) | → | mark(U21(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)) | |
| active(isNeList(V)) | → | mark(U31(isPalListKind(V), V)) | active(isNeList(__(V1, V2))) | → | mark(U41(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)) | |
| active(isNeList(__(V1, V2))) | → | mark(U51(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)) | active(isNePal(V)) | → | mark(U61(isPalListKind(V), V)) | |
| active(isNePal(__(I, __(P, I)))) | → | mark(and(and(isQid(I), isPalListKind(I)), and(isPal(P), isPalListKind(P)))) | active(isPal(V)) | → | mark(U71(isPalListKind(V), V)) | |
| active(isPal(nil)) | → | mark(tt) | active(isPalListKind(a)) | → | mark(tt) | |
| active(isPalListKind(e)) | → | mark(tt) | active(isPalListKind(i)) | → | mark(tt) | |
| active(isPalListKind(nil)) | → | mark(tt) | active(isPalListKind(o)) | → | mark(tt) | |
| active(isPalListKind(u)) | → | mark(tt) | active(isPalListKind(__(V1, V2))) | → | mark(and(isPalListKind(V1), isPalListKind(V2))) | |
| active(isQid(a)) | → | mark(tt) | active(isQid(e)) | → | mark(tt) | |
| active(isQid(i)) | → | mark(tt) | active(isQid(o)) | → | mark(tt) | |
| active(isQid(u)) | → | mark(tt) | active(__(X1, X2)) | → | __(active(X1), X2) | |
| active(__(X1, X2)) | → | __(X1, active(X2)) | active(U11(X1, X2)) | → | U11(active(X1), X2) | |
| active(U12(X)) | → | U12(active(X)) | active(U21(X1, X2, X3)) | → | U21(active(X1), X2, X3) | |
| active(U22(X1, X2)) | → | U22(active(X1), X2) | active(U23(X)) | → | U23(active(X)) | |
| active(U31(X1, X2)) | → | U31(active(X1), X2) | active(U32(X)) | → | U32(active(X)) | |
| active(U41(X1, X2, X3)) | → | U41(active(X1), X2, X3) | active(U42(X1, X2)) | → | U42(active(X1), X2) | |
| active(U43(X)) | → | U43(active(X)) | active(U51(X1, X2, X3)) | → | U51(active(X1), X2, X3) | |
| active(U52(X1, X2)) | → | U52(active(X1), X2) | active(U53(X)) | → | U53(active(X)) | |
| active(U61(X1, X2)) | → | U61(active(X1), X2) | active(U62(X)) | → | U62(active(X)) | |
| active(U71(X1, X2)) | → | U71(active(X1), X2) | active(U72(X)) | → | U72(active(X)) | |
| active(and(X1, X2)) | → | and(active(X1), X2) | __(mark(X1), X2) | → | mark(__(X1, X2)) | |
| __(X1, mark(X2)) | → | mark(__(X1, X2)) | U11(mark(X1), X2) | → | mark(U11(X1, X2)) | |
| U12(mark(X)) | → | mark(U12(X)) | U21(mark(X1), X2, X3) | → | mark(U21(X1, X2, X3)) | |
| U22(mark(X1), X2) | → | mark(U22(X1, X2)) | U23(mark(X)) | → | mark(U23(X)) | |
| U31(mark(X1), X2) | → | mark(U31(X1, X2)) | U32(mark(X)) | → | mark(U32(X)) | |
| U41(mark(X1), X2, X3) | → | mark(U41(X1, X2, X3)) | U42(mark(X1), X2) | → | mark(U42(X1, X2)) | |
| U43(mark(X)) | → | mark(U43(X)) | U51(mark(X1), X2, X3) | → | mark(U51(X1, X2, X3)) | |
| U52(mark(X1), X2) | → | mark(U52(X1, X2)) | U53(mark(X)) | → | mark(U53(X)) | |
| U61(mark(X1), X2) | → | mark(U61(X1, X2)) | U62(mark(X)) | → | mark(U62(X)) | |
| U71(mark(X1), X2) | → | mark(U71(X1, X2)) | U72(mark(X)) | → | mark(U72(X)) | |
| and(mark(X1), X2) | → | mark(and(X1, X2)) | proper(__(X1, X2)) | → | __(proper(X1), proper(X2)) | |
| proper(nil) | → | ok(nil) | proper(U11(X1, X2)) | → | U11(proper(X1), proper(X2)) | |
| proper(tt) | → | ok(tt) | proper(U12(X)) | → | U12(proper(X)) | |
| proper(isNeList(X)) | → | isNeList(proper(X)) | proper(U21(X1, X2, X3)) | → | U21(proper(X1), proper(X2), proper(X3)) | |
| proper(U22(X1, X2)) | → | U22(proper(X1), proper(X2)) | proper(isList(X)) | → | isList(proper(X)) | |
| proper(U23(X)) | → | U23(proper(X)) | proper(U31(X1, X2)) | → | U31(proper(X1), proper(X2)) | |
| proper(U32(X)) | → | U32(proper(X)) | proper(isQid(X)) | → | isQid(proper(X)) | |
| proper(U41(X1, X2, X3)) | → | U41(proper(X1), proper(X2), proper(X3)) | proper(U42(X1, X2)) | → | U42(proper(X1), proper(X2)) | |
| proper(U43(X)) | → | U43(proper(X)) | proper(U51(X1, X2, X3)) | → | U51(proper(X1), proper(X2), proper(X3)) | |
| proper(U52(X1, X2)) | → | U52(proper(X1), proper(X2)) | proper(U53(X)) | → | U53(proper(X)) | |
| proper(U61(X1, X2)) | → | U61(proper(X1), proper(X2)) | proper(U62(X)) | → | U62(proper(X)) | |
| proper(U71(X1, X2)) | → | U71(proper(X1), proper(X2)) | proper(U72(X)) | → | U72(proper(X)) | |
| proper(isNePal(X)) | → | isNePal(proper(X)) | proper(and(X1, X2)) | → | and(proper(X1), proper(X2)) | |
| proper(isPalListKind(X)) | → | isPalListKind(proper(X)) | proper(isPal(X)) | → | isPal(proper(X)) | |
| proper(a) | → | ok(a) | proper(e) | → | ok(e) | |
| proper(i) | → | ok(i) | proper(o) | → | ok(o) | |
| proper(u) | → | ok(u) | __(ok(X1), ok(X2)) | → | ok(__(X1, X2)) | |
| U11(ok(X1), ok(X2)) | → | ok(U11(X1, X2)) | U12(ok(X)) | → | ok(U12(X)) | |
| isNeList(ok(X)) | → | ok(isNeList(X)) | U21(ok(X1), ok(X2), ok(X3)) | → | ok(U21(X1, X2, X3)) | |
| U22(ok(X1), ok(X2)) | → | ok(U22(X1, X2)) | isList(ok(X)) | → | ok(isList(X)) | |
| U23(ok(X)) | → | ok(U23(X)) | U31(ok(X1), ok(X2)) | → | ok(U31(X1, X2)) | |
| U32(ok(X)) | → | ok(U32(X)) | isQid(ok(X)) | → | ok(isQid(X)) | |
| U41(ok(X1), ok(X2), ok(X3)) | → | ok(U41(X1, X2, X3)) | U42(ok(X1), ok(X2)) | → | ok(U42(X1, X2)) | |
| U43(ok(X)) | → | ok(U43(X)) | U51(ok(X1), ok(X2), ok(X3)) | → | ok(U51(X1, X2, X3)) | |
| U52(ok(X1), ok(X2)) | → | ok(U52(X1, X2)) | U53(ok(X)) | → | ok(U53(X)) | |
| U61(ok(X1), ok(X2)) | → | ok(U61(X1, X2)) | U62(ok(X)) | → | ok(U62(X)) | |
| U71(ok(X1), ok(X2)) | → | ok(U71(X1, X2)) | U72(ok(X)) | → | ok(U72(X)) | |
| isNePal(ok(X)) | → | ok(isNePal(X)) | and(ok(X1), ok(X2)) | → | ok(and(X1, X2)) | |
| isPalListKind(ok(X)) | → | ok(isPalListKind(X)) | isPal(ok(X)) | → | ok(isPal(X)) | |
| top(mark(X)) | → | top(proper(X)) | top(ok(X)) | → | top(active(X)) |
Termination of terms over the following signature is verified: isList, isNeList, __, U62, U43, U61, U42, U41, isNePal, ok, proper, U23, U21, top, U22, e, isPalListKind, a, o, mark, isPal, i, and, U71, U72, u, U51, tt, U53, U52, U11, active, U12, isQid, U31, U32, nil