0 QTRS
↳1 DependencyPairsProof (⇔)
↳2 QDP
↳3 DependencyGraphProof (⇔)
↳4 AND
↳5 QDP
↳6 QDPSizeChangeProof (⇔)
↳7 TRUE
↳8 QDP
↳9 QDPSizeChangeProof (⇔)
↳10 TRUE
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) → U121(tt, activate(M), activate(N))
U111(tt, M, N) → ACTIVATE(M)
U111(tt, M, N) → ACTIVATE(N)
U121(tt, M, N) → PLUS(activate(N), activate(M))
U121(tt, M, N) → ACTIVATE(N)
U121(tt, M, N) → ACTIVATE(M)
U211(tt, M, N) → U221(tt, activate(M), activate(N))
U211(tt, M, N) → ACTIVATE(M)
U211(tt, M, N) → ACTIVATE(N)
U221(tt, M, N) → PLUS(x(activate(N), activate(M)), activate(N))
U221(tt, M, N) → X(activate(N), activate(M))
U221(tt, M, N) → ACTIVATE(N)
U221(tt, M, N) → ACTIVATE(M)
PLUS(N, s(M)) → U111(tt, M, N)
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
U121(tt, M, N) → PLUS(activate(N), activate(M))
PLUS(N, s(M)) → U111(tt, M, N)
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
Order:Combined order from the following AFS and order.
activate(x1) = x1
tt = tt
s(x1) = s(x1)
Lexicographic path order with status [LPO].
Quasi-Precedence:
trivial
tt: []
s1: [1]
AFS:
activate(x1) = x1
tt = tt
s(x1) = s(x1)
From the DPs we obtained the following set of size-change graphs:
We oriented the following set of usable rules [AAECC05,FROCOS05].
activate(X) → X
U221(tt, M, N) → X(activate(N), activate(M))
X(N, s(M)) → U211(tt, M, N)
U211(tt, M, N) → U221(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
Order:Combined order from the following AFS and order.
activate(x1) = x1
tt = tt
s(x1) = s(x1)
Lexicographic path order with status [LPO].
Quasi-Precedence:
trivial
tt: []
s1: [1]
AFS:
activate(x1) = x1
tt = tt
s(x1) = s(x1)
From the DPs we obtained the following set of size-change graphs:
We oriented the following set of usable rules [AAECC05,FROCOS05].
activate(X) → X