YES

The TRS could be proven terminating. The proof took 798 ms.

The following DP Processors were used


Problem 1 was processed with processor DependencyGraph (78ms).
 | – Problem 2 was processed with processor PolynomialLinearRange4iUR (170ms).
 |    | – Problem 4 was processed with processor DependencyGraph (1ms).
 | – Problem 3 was processed with processor PolynomialLinearRange4iUR (117ms).
 |    | – Problem 5 was processed with processor DependencyGraph (36ms).

Problem 1: DependencyGraph



Dependency Pair Problem

Dependency Pairs

U12#(tt, M, N)activate#(M)U11#(tt, M, N)U12#(tt, activate(M), activate(N))
U11#(tt, M, N)activate#(M)x#(N, s(M))U21#(tt, M, N)
U21#(tt, M, N)activate#(N)U22#(tt, M, N)x#(activate(N), activate(M))
U12#(tt, M, N)activate#(N)U22#(tt, M, N)plus#(x(activate(N), activate(M)), activate(N))
U22#(tt, M, N)activate#(M)U12#(tt, M, N)plus#(activate(N), activate(M))
U21#(tt, M, N)activate#(M)U22#(tt, M, N)activate#(N)
U21#(tt, M, N)U22#(tt, activate(M), activate(N))U11#(tt, M, N)activate#(N)
plus#(N, s(M))U11#(tt, M, N)

Rewrite Rules

U11(tt, M, N)U12(tt, activate(M), activate(N))U12(tt, M, N)s(plus(activate(N), activate(M)))
U21(tt, M, N)U22(tt, activate(M), activate(N))U22(tt, M, N)plus(x(activate(N), activate(M)), activate(N))
plus(N, 0)Nplus(N, s(M))U11(tt, M, N)
x(N, 0)0x(N, s(M))U21(tt, M, N)
activate(X)X

Original Signature

Termination of terms over the following signature is verified: activate, plus, 0, s, tt, U11, U12, U21, U22, x

Strategy


The following SCCs where found

U22#(tt, M, N) → x#(activate(N), activate(M))U21#(tt, M, N) → U22#(tt, activate(M), activate(N))
x#(N, s(M)) → U21#(tt, M, N)

U12#(tt, M, N) → plus#(activate(N), activate(M))U11#(tt, M, N) → U12#(tt, activate(M), activate(N))
plus#(N, s(M)) → U11#(tt, M, N)

Problem 2: PolynomialLinearRange4iUR



Dependency Pair Problem

Dependency Pairs

U12#(tt, M, N)plus#(activate(N), activate(M))U11#(tt, M, N)U12#(tt, activate(M), activate(N))
plus#(N, s(M))U11#(tt, M, N)

Rewrite Rules

U11(tt, M, N)U12(tt, activate(M), activate(N))U12(tt, M, N)s(plus(activate(N), activate(M)))
U21(tt, M, N)U22(tt, activate(M), activate(N))U22(tt, M, N)plus(x(activate(N), activate(M)), activate(N))
plus(N, 0)Nplus(N, s(M))U11(tt, M, N)
x(N, 0)0x(N, s(M))U21(tt, M, N)
activate(X)X

Original Signature

Termination of terms over the following signature is verified: activate, plus, 0, s, tt, U11, U12, U21, U22, x

Strategy


Polynomial Interpretation

Improved Usable rules

activate(X)X

The following dependency pairs are strictly oriented by an ordering on the given polynomial interpretation, thus they are removed:

plus#(N, s(M))U11#(tt, M, N)

Problem 4: DependencyGraph



Dependency Pair Problem

Dependency Pairs

U12#(tt, M, N)plus#(activate(N), activate(M))U11#(tt, M, N)U12#(tt, activate(M), activate(N))

Rewrite Rules

U11(tt, M, N)U12(tt, activate(M), activate(N))U12(tt, M, N)s(plus(activate(N), activate(M)))
U21(tt, M, N)U22(tt, activate(M), activate(N))U22(tt, M, N)plus(x(activate(N), activate(M)), activate(N))
plus(N, 0)Nplus(N, s(M))U11(tt, M, N)
x(N, 0)0x(N, s(M))U21(tt, M, N)
activate(X)X

Original Signature

Termination of terms over the following signature is verified: activate, plus, 0, s, tt, U11, U12, U21, x, U22

Strategy


There are no SCCs!

Problem 3: PolynomialLinearRange4iUR



Dependency Pair Problem

Dependency Pairs

U22#(tt, M, N)x#(activate(N), activate(M))U21#(tt, M, N)U22#(tt, activate(M), activate(N))
x#(N, s(M))U21#(tt, M, N)

Rewrite Rules

U11(tt, M, N)U12(tt, activate(M), activate(N))U12(tt, M, N)s(plus(activate(N), activate(M)))
U21(tt, M, N)U22(tt, activate(M), activate(N))U22(tt, M, N)plus(x(activate(N), activate(M)), activate(N))
plus(N, 0)Nplus(N, s(M))U11(tt, M, N)
x(N, 0)0x(N, s(M))U21(tt, M, N)
activate(X)X

Original Signature

Termination of terms over the following signature is verified: activate, plus, 0, s, tt, U11, U12, U21, U22, x

Strategy


Polynomial Interpretation

Improved Usable rules

activate(X)X

The following dependency pairs are strictly oriented by an ordering on the given polynomial interpretation, thus they are removed:

x#(N, s(M))U21#(tt, M, N)

Problem 5: DependencyGraph



Dependency Pair Problem

Dependency Pairs

U22#(tt, M, N)x#(activate(N), activate(M))U21#(tt, M, N)U22#(tt, activate(M), activate(N))

Rewrite Rules

U11(tt, M, N)U12(tt, activate(M), activate(N))U12(tt, M, N)s(plus(activate(N), activate(M)))
U21(tt, M, N)U22(tt, activate(M), activate(N))U22(tt, M, N)plus(x(activate(N), activate(M)), activate(N))
plus(N, 0)Nplus(N, s(M))U11(tt, M, N)
x(N, 0)0x(N, s(M))U21(tt, M, N)
activate(X)X

Original Signature

Termination of terms over the following signature is verified: activate, plus, 0, s, tt, U11, U12, U21, x, U22

Strategy


There are no SCCs!