LMPO
MAYBE
We consider the following Problem:
Strict Trs:
{ a__U11(tt(), M, N) -> a__U12(tt(), M, N)
, a__U12(tt(), M, N) -> s(a__plus(mark(N), mark(M)))
, a__U21(tt(), M, N) -> a__U22(tt(), M, N)
, a__U22(tt(), M, N) -> a__plus(a__x(mark(N), mark(M)), mark(N))
, a__plus(N, 0()) -> mark(N)
, a__plus(N, s(M)) -> a__U11(tt(), M, N)
, a__x(N, 0()) -> 0()
, a__x(N, s(M)) -> a__U21(tt(), M, N)
, mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3)
, mark(U12(X1, X2, X3)) -> a__U12(mark(X1), X2, X3)
, mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2))
, mark(U21(X1, X2, X3)) -> a__U21(mark(X1), X2, X3)
, mark(U22(X1, X2, X3)) -> a__U22(mark(X1), X2, X3)
, mark(x(X1, X2)) -> a__x(mark(X1), mark(X2))
, mark(tt()) -> tt()
, mark(s(X)) -> s(mark(X))
, mark(0()) -> 0()
, a__U11(X1, X2, X3) -> U11(X1, X2, X3)
, a__U12(X1, X2, X3) -> U12(X1, X2, X3)
, a__plus(X1, X2) -> plus(X1, X2)
, a__U21(X1, X2, X3) -> U21(X1, X2, X3)
, a__U22(X1, X2, X3) -> U22(X1, X2, X3)
, a__x(X1, X2) -> x(X1, X2)}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
MPO
MAYBE
We consider the following Problem:
Strict Trs:
{ a__U11(tt(), M, N) -> a__U12(tt(), M, N)
, a__U12(tt(), M, N) -> s(a__plus(mark(N), mark(M)))
, a__U21(tt(), M, N) -> a__U22(tt(), M, N)
, a__U22(tt(), M, N) -> a__plus(a__x(mark(N), mark(M)), mark(N))
, a__plus(N, 0()) -> mark(N)
, a__plus(N, s(M)) -> a__U11(tt(), M, N)
, a__x(N, 0()) -> 0()
, a__x(N, s(M)) -> a__U21(tt(), M, N)
, mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3)
, mark(U12(X1, X2, X3)) -> a__U12(mark(X1), X2, X3)
, mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2))
, mark(U21(X1, X2, X3)) -> a__U21(mark(X1), X2, X3)
, mark(U22(X1, X2, X3)) -> a__U22(mark(X1), X2, X3)
, mark(x(X1, X2)) -> a__x(mark(X1), mark(X2))
, mark(tt()) -> tt()
, mark(s(X)) -> s(mark(X))
, mark(0()) -> 0()
, a__U11(X1, X2, X3) -> U11(X1, X2, X3)
, a__U12(X1, X2, X3) -> U12(X1, X2, X3)
, a__plus(X1, X2) -> plus(X1, X2)
, a__U21(X1, X2, X3) -> U21(X1, X2, X3)
, a__U22(X1, X2, X3) -> U22(X1, X2, X3)
, a__x(X1, X2) -> x(X1, X2)}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
POP*
MAYBE
We consider the following Problem:
Strict Trs:
{ a__U11(tt(), M, N) -> a__U12(tt(), M, N)
, a__U12(tt(), M, N) -> s(a__plus(mark(N), mark(M)))
, a__U21(tt(), M, N) -> a__U22(tt(), M, N)
, a__U22(tt(), M, N) -> a__plus(a__x(mark(N), mark(M)), mark(N))
, a__plus(N, 0()) -> mark(N)
, a__plus(N, s(M)) -> a__U11(tt(), M, N)
, a__x(N, 0()) -> 0()
, a__x(N, s(M)) -> a__U21(tt(), M, N)
, mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3)
, mark(U12(X1, X2, X3)) -> a__U12(mark(X1), X2, X3)
, mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2))
, mark(U21(X1, X2, X3)) -> a__U21(mark(X1), X2, X3)
, mark(U22(X1, X2, X3)) -> a__U22(mark(X1), X2, X3)
, mark(x(X1, X2)) -> a__x(mark(X1), mark(X2))
, mark(tt()) -> tt()
, mark(s(X)) -> s(mark(X))
, mark(0()) -> 0()
, a__U11(X1, X2, X3) -> U11(X1, X2, X3)
, a__U12(X1, X2, X3) -> U12(X1, X2, X3)
, a__plus(X1, X2) -> plus(X1, X2)
, a__U21(X1, X2, X3) -> U21(X1, X2, X3)
, a__U22(X1, X2, X3) -> U22(X1, X2, X3)
, a__x(X1, X2) -> x(X1, X2)}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
POP* (PS)
MAYBE
We consider the following Problem:
Strict Trs:
{ a__U11(tt(), M, N) -> a__U12(tt(), M, N)
, a__U12(tt(), M, N) -> s(a__plus(mark(N), mark(M)))
, a__U21(tt(), M, N) -> a__U22(tt(), M, N)
, a__U22(tt(), M, N) -> a__plus(a__x(mark(N), mark(M)), mark(N))
, a__plus(N, 0()) -> mark(N)
, a__plus(N, s(M)) -> a__U11(tt(), M, N)
, a__x(N, 0()) -> 0()
, a__x(N, s(M)) -> a__U21(tt(), M, N)
, mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3)
, mark(U12(X1, X2, X3)) -> a__U12(mark(X1), X2, X3)
, mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2))
, mark(U21(X1, X2, X3)) -> a__U21(mark(X1), X2, X3)
, mark(U22(X1, X2, X3)) -> a__U22(mark(X1), X2, X3)
, mark(x(X1, X2)) -> a__x(mark(X1), mark(X2))
, mark(tt()) -> tt()
, mark(s(X)) -> s(mark(X))
, mark(0()) -> 0()
, a__U11(X1, X2, X3) -> U11(X1, X2, X3)
, a__U12(X1, X2, X3) -> U12(X1, X2, X3)
, a__plus(X1, X2) -> plus(X1, X2)
, a__U21(X1, X2, X3) -> U21(X1, X2, X3)
, a__U22(X1, X2, X3) -> U22(X1, X2, X3)
, a__x(X1, X2) -> x(X1, X2)}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
Small POP*
MAYBE
We consider the following Problem:
Strict Trs:
{ a__U11(tt(), M, N) -> a__U12(tt(), M, N)
, a__U12(tt(), M, N) -> s(a__plus(mark(N), mark(M)))
, a__U21(tt(), M, N) -> a__U22(tt(), M, N)
, a__U22(tt(), M, N) -> a__plus(a__x(mark(N), mark(M)), mark(N))
, a__plus(N, 0()) -> mark(N)
, a__plus(N, s(M)) -> a__U11(tt(), M, N)
, a__x(N, 0()) -> 0()
, a__x(N, s(M)) -> a__U21(tt(), M, N)
, mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3)
, mark(U12(X1, X2, X3)) -> a__U12(mark(X1), X2, X3)
, mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2))
, mark(U21(X1, X2, X3)) -> a__U21(mark(X1), X2, X3)
, mark(U22(X1, X2, X3)) -> a__U22(mark(X1), X2, X3)
, mark(x(X1, X2)) -> a__x(mark(X1), mark(X2))
, mark(tt()) -> tt()
, mark(s(X)) -> s(mark(X))
, mark(0()) -> 0()
, a__U11(X1, X2, X3) -> U11(X1, X2, X3)
, a__U12(X1, X2, X3) -> U12(X1, X2, X3)
, a__plus(X1, X2) -> plus(X1, X2)
, a__U21(X1, X2, X3) -> U21(X1, X2, X3)
, a__U22(X1, X2, X3) -> U22(X1, X2, X3)
, a__x(X1, X2) -> x(X1, X2)}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
Small POP* (PS)
MAYBE
We consider the following Problem:
Strict Trs:
{ a__U11(tt(), M, N) -> a__U12(tt(), M, N)
, a__U12(tt(), M, N) -> s(a__plus(mark(N), mark(M)))
, a__U21(tt(), M, N) -> a__U22(tt(), M, N)
, a__U22(tt(), M, N) -> a__plus(a__x(mark(N), mark(M)), mark(N))
, a__plus(N, 0()) -> mark(N)
, a__plus(N, s(M)) -> a__U11(tt(), M, N)
, a__x(N, 0()) -> 0()
, a__x(N, s(M)) -> a__U21(tt(), M, N)
, mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3)
, mark(U12(X1, X2, X3)) -> a__U12(mark(X1), X2, X3)
, mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2))
, mark(U21(X1, X2, X3)) -> a__U21(mark(X1), X2, X3)
, mark(U22(X1, X2, X3)) -> a__U22(mark(X1), X2, X3)
, mark(x(X1, X2)) -> a__x(mark(X1), mark(X2))
, mark(tt()) -> tt()
, mark(s(X)) -> s(mark(X))
, mark(0()) -> 0()
, a__U11(X1, X2, X3) -> U11(X1, X2, X3)
, a__U12(X1, X2, X3) -> U12(X1, X2, X3)
, a__plus(X1, X2) -> plus(X1, X2)
, a__U21(X1, X2, X3) -> U21(X1, X2, X3)
, a__U22(X1, X2, X3) -> U22(X1, X2, X3)
, a__x(X1, X2) -> x(X1, X2)}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..