U11(tt, M, N) → U12(tt, activate(M), activate(N))
U12(tt, M, N) → s(plus(activate(N), activate(M)))
plus(N, 0) → N
plus(N, s(M)) → U11(tt, M, N)
activate(X) → X
↳ QTRS
↳ DependencyPairsProof
U11(tt, M, N) → U12(tt, activate(M), activate(N))
U12(tt, M, N) → s(plus(activate(N), activate(M)))
plus(N, 0) → N
plus(N, s(M)) → U11(tt, M, N)
activate(X) → X
PLUS(N, s(M)) → U111(tt, M, N)
U111(tt, M, N) → ACTIVATE(N)
U121(tt, M, N) → ACTIVATE(N)
U121(tt, M, N) → PLUS(activate(N), activate(M))
U121(tt, M, N) → ACTIVATE(M)
U111(tt, M, N) → ACTIVATE(M)
U111(tt, M, N) → U121(tt, activate(M), activate(N))
U11(tt, M, N) → U12(tt, activate(M), activate(N))
U12(tt, M, N) → s(plus(activate(N), activate(M)))
plus(N, 0) → N
plus(N, s(M)) → U11(tt, M, N)
activate(X) → X
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
PLUS(N, s(M)) → U111(tt, M, N)
U111(tt, M, N) → ACTIVATE(N)
U121(tt, M, N) → ACTIVATE(N)
U121(tt, M, N) → PLUS(activate(N), activate(M))
U121(tt, M, N) → ACTIVATE(M)
U111(tt, M, N) → ACTIVATE(M)
U111(tt, M, N) → U121(tt, activate(M), activate(N))
U11(tt, M, N) → U12(tt, activate(M), activate(N))
U12(tt, M, N) → s(plus(activate(N), activate(M)))
plus(N, 0) → N
plus(N, s(M)) → U11(tt, M, N)
activate(X) → X
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
PLUS(N, s(M)) → U111(tt, M, N)
U121(tt, M, N) → PLUS(activate(N), activate(M))
U111(tt, M, N) → U121(tt, activate(M), activate(N))
U11(tt, M, N) → U12(tt, activate(M), activate(N))
U12(tt, M, N) → s(plus(activate(N), activate(M)))
plus(N, 0) → N
plus(N, s(M)) → U11(tt, M, N)
activate(X) → X
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
PLUS(N, s(M)) → U111(tt, M, N)
Used ordering: Polynomial interpretation [25,35]:
U121(tt, M, N) → PLUS(activate(N), activate(M))
U111(tt, M, N) → U121(tt, activate(M), activate(N))
The value of delta used in the strict ordering is 1/2.
POL(PLUS(x1, x2)) = 3/2 + (2)x_2
POL(U121(x1, x2, x3)) = 1/2 + (4)x_1 + (13/4)x_2
POL(tt) = 1/4
POL(U111(x1, x2, x3)) = 3/2 + (13/4)x_2
POL(s(x1)) = 1/4 + (4)x_1
POL(activate(x1)) = x_1
activate(X) → X
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
U121(tt, M, N) → PLUS(activate(N), activate(M))
U111(tt, M, N) → U121(tt, activate(M), activate(N))
U11(tt, M, N) → U12(tt, activate(M), activate(N))
U12(tt, M, N) → s(plus(activate(N), activate(M)))
plus(N, 0) → N
plus(N, s(M)) → U11(tt, M, N)
activate(X) → X