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) → N
plus(N, s(M)) → U11(tt, M, N)
x(N, 0) → 0
x(N, s(M)) → U21(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)))
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) → N
plus(N, s(M)) → U11(tt, M, N)
x(N, 0) → 0
x(N, s(M)) → U21(tt, M, N)
activate(X) → X
U111(tt, M, N) → ACTIVATE(N)
U221(tt, M, N) → ACTIVATE(N)
U211(tt, M, N) → U221(tt, activate(M), activate(N))
U221(tt, M, N) → ACTIVATE(M)
U121(tt, M, N) → PLUS(activate(N), activate(M))
U111(tt, M, N) → ACTIVATE(M)
U221(tt, M, N) → X(activate(N), activate(M))
X(N, s(M)) → U211(tt, M, N)
U111(tt, M, N) → U121(tt, activate(M), activate(N))
U211(tt, M, N) → ACTIVATE(M)
PLUS(N, s(M)) → U111(tt, M, N)
U221(tt, M, N) → PLUS(x(activate(N), activate(M)), activate(N))
U211(tt, M, N) → ACTIVATE(N)
U121(tt, M, N) → ACTIVATE(N)
U121(tt, M, N) → ACTIVATE(M)
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) → N
plus(N, s(M)) → U11(tt, M, N)
x(N, 0) → 0
x(N, s(M)) → U21(tt, M, N)
activate(X) → X
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
U111(tt, M, N) → ACTIVATE(N)
U221(tt, M, N) → ACTIVATE(N)
U211(tt, M, N) → U221(tt, activate(M), activate(N))
U221(tt, M, N) → ACTIVATE(M)
U121(tt, M, N) → PLUS(activate(N), activate(M))
U111(tt, M, N) → ACTIVATE(M)
U221(tt, M, N) → X(activate(N), activate(M))
X(N, s(M)) → U211(tt, M, N)
U111(tt, M, N) → U121(tt, activate(M), activate(N))
U211(tt, M, N) → ACTIVATE(M)
PLUS(N, s(M)) → U111(tt, M, N)
U221(tt, M, N) → PLUS(x(activate(N), activate(M)), activate(N))
U211(tt, M, N) → ACTIVATE(N)
U121(tt, M, N) → ACTIVATE(N)
U121(tt, M, N) → ACTIVATE(M)
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) → N
plus(N, s(M)) → U11(tt, M, N)
x(N, 0) → 0
x(N, s(M)) → U21(tt, M, N)
activate(X) → X
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
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)))
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) → N
plus(N, s(M)) → U11(tt, M, N)
x(N, 0) → 0
x(N, s(M)) → U21(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)
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.
POL(PLUS(x1, x2)) = 2 + (3)x_2
POL(U121(x1, x2, x3)) = 3 + (4)x_2
POL(tt) = 3
POL(U111(x1, x2, x3)) = 1 + x_1 + (4)x_2
POL(s(x1)) = 3 + (4)x_1
POL(activate(x1)) = x_1
activate(X) → X
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
↳ QDP
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) → N
plus(N, s(M)) → U11(tt, M, N)
x(N, 0) → 0
x(N, s(M)) → U21(tt, M, N)
activate(X) → X
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
U211(tt, M, N) → U221(tt, activate(M), activate(N))
U221(tt, M, N) → X(activate(N), activate(M))
X(N, s(M)) → U211(tt, M, N)
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) → N
plus(N, s(M)) → U11(tt, M, N)
x(N, 0) → 0
x(N, s(M)) → U21(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.
U211(tt, M, N) → U221(tt, activate(M), activate(N))
U221(tt, M, N) → X(activate(N), activate(M))
X(N, s(M)) → U211(tt, M, N)
The value of delta used in the strict ordering is 1.
POL(X(x1, x2)) = 1 + (2)x_2
POL(tt) = 1
POL(U221(x1, x2, x3)) = (2)x_1 + (2)x_2
POL(activate(x1)) = x_1
POL(s(x1)) = 4 + (4)x_1
POL(U211(x1, x2, x3)) = 3 + (4)x_2
activate(X) → X
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
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) → N
plus(N, s(M)) → U11(tt, M, N)
x(N, 0) → 0
x(N, s(M)) → U21(tt, M, N)
activate(X) → X