lt(0, s(x)) → true
lt(x, 0) → false
lt(s(x), s(y)) → lt(x, y)
minus(x, y) → help(lt(y, x), x, y)
help(true, x, y) → s(minus(x, s(y)))
help(false, x, y) → 0
↳ QTRS
↳ DependencyPairsProof
lt(0, s(x)) → true
lt(x, 0) → false
lt(s(x), s(y)) → lt(x, y)
minus(x, y) → help(lt(y, x), x, y)
help(true, x, y) → s(minus(x, s(y)))
help(false, x, y) → 0
MINUS(x, y) → LT(y, x)
LT(s(x), s(y)) → LT(x, y)
MINUS(x, y) → HELP(lt(y, x), x, y)
HELP(true, x, y) → MINUS(x, s(y))
lt(0, s(x)) → true
lt(x, 0) → false
lt(s(x), s(y)) → lt(x, y)
minus(x, y) → help(lt(y, x), x, y)
help(true, x, y) → s(minus(x, s(y)))
help(false, x, y) → 0
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
MINUS(x, y) → LT(y, x)
LT(s(x), s(y)) → LT(x, y)
MINUS(x, y) → HELP(lt(y, x), x, y)
HELP(true, x, y) → MINUS(x, s(y))
lt(0, s(x)) → true
lt(x, 0) → false
lt(s(x), s(y)) → lt(x, y)
minus(x, y) → help(lt(y, x), x, y)
help(true, x, y) → s(minus(x, s(y)))
help(false, x, y) → 0
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
LT(s(x), s(y)) → LT(x, y)
lt(0, s(x)) → true
lt(x, 0) → false
lt(s(x), s(y)) → lt(x, y)
minus(x, y) → help(lt(y, x), x, y)
help(true, x, y) → s(minus(x, s(y)))
help(false, x, y) → 0
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
LT(s(x), s(y)) → LT(x, y)
The value of delta used in the strict ordering is 1.
POL(s(x1)) = 1 + x_1
POL(LT(x1, x2)) = x_2
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
↳ QDP
lt(0, s(x)) → true
lt(x, 0) → false
lt(s(x), s(y)) → lt(x, y)
minus(x, y) → help(lt(y, x), x, y)
help(true, x, y) → s(minus(x, s(y)))
help(false, x, y) → 0
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
MINUS(x, y) → HELP(lt(y, x), x, y)
HELP(true, x, y) → MINUS(x, s(y))
lt(0, s(x)) → true
lt(x, 0) → false
lt(s(x), s(y)) → lt(x, y)
minus(x, y) → help(lt(y, x), x, y)
help(true, x, y) → s(minus(x, s(y)))
help(false, x, y) → 0