f(0) → true
f(1) → false
f(s(x)) → f(x)
if(true, s(x), s(y)) → s(x)
if(false, s(x), s(y)) → s(y)
g(x, c(y)) → c(g(x, y))
g(x, c(y)) → g(x, if(f(x), c(g(s(x), y)), c(y)))
↳ QTRS
↳ DependencyPairsProof
f(0) → true
f(1) → false
f(s(x)) → f(x)
if(true, s(x), s(y)) → s(x)
if(false, s(x), s(y)) → s(y)
g(x, c(y)) → c(g(x, y))
g(x, c(y)) → g(x, if(f(x), c(g(s(x), y)), c(y)))
G(x, c(y)) → G(x, if(f(x), c(g(s(x), y)), c(y)))
F(s(x)) → F(x)
G(x, c(y)) → F(x)
G(x, c(y)) → G(s(x), y)
G(x, c(y)) → IF(f(x), c(g(s(x), y)), c(y))
G(x, c(y)) → G(x, y)
f(0) → true
f(1) → false
f(s(x)) → f(x)
if(true, s(x), s(y)) → s(x)
if(false, s(x), s(y)) → s(y)
g(x, c(y)) → c(g(x, y))
g(x, c(y)) → g(x, if(f(x), c(g(s(x), y)), c(y)))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
G(x, c(y)) → G(x, if(f(x), c(g(s(x), y)), c(y)))
F(s(x)) → F(x)
G(x, c(y)) → F(x)
G(x, c(y)) → G(s(x), y)
G(x, c(y)) → IF(f(x), c(g(s(x), y)), c(y))
G(x, c(y)) → G(x, y)
f(0) → true
f(1) → false
f(s(x)) → f(x)
if(true, s(x), s(y)) → s(x)
if(false, s(x), s(y)) → s(y)
g(x, c(y)) → c(g(x, y))
g(x, c(y)) → g(x, if(f(x), c(g(s(x), y)), c(y)))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
F(s(x)) → F(x)
f(0) → true
f(1) → false
f(s(x)) → f(x)
if(true, s(x), s(y)) → s(x)
if(false, s(x), s(y)) → s(y)
g(x, c(y)) → c(g(x, y))
g(x, c(y)) → g(x, if(f(x), c(g(s(x), y)), c(y)))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
F(s(x)) → F(x)
The value of delta used in the strict ordering is 1/16.
POL(s(x1)) = 1/4 + (2)x_1
POL(F(x1)) = (1/4)x_1
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
↳ QDP
f(0) → true
f(1) → false
f(s(x)) → f(x)
if(true, s(x), s(y)) → s(x)
if(false, s(x), s(y)) → s(y)
g(x, c(y)) → c(g(x, y))
g(x, c(y)) → g(x, if(f(x), c(g(s(x), y)), c(y)))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
G(x, c(y)) → G(s(x), y)
G(x, c(y)) → G(x, y)
f(0) → true
f(1) → false
f(s(x)) → f(x)
if(true, s(x), s(y)) → s(x)
if(false, s(x), s(y)) → s(y)
g(x, c(y)) → c(g(x, y))
g(x, c(y)) → g(x, if(f(x), c(g(s(x), y)), c(y)))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
G(x, c(y)) → G(x, y)
Used ordering: Polynomial interpretation [25,35]:
G(x, c(y)) → G(s(x), y)
The value of delta used in the strict ordering is 4.
POL(c(x1)) = 1 + (2)x_1
POL(s(x1)) = 4
POL(G(x1, x2)) = x_1 + (4)x_2
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
G(x, c(y)) → G(s(x), y)
f(0) → true
f(1) → false
f(s(x)) → f(x)
if(true, s(x), s(y)) → s(x)
if(false, s(x), s(y)) → s(y)
g(x, c(y)) → c(g(x, y))
g(x, c(y)) → g(x, if(f(x), c(g(s(x), y)), c(y)))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
G(x, c(y)) → G(s(x), y)
The value of delta used in the strict ordering is 16.
POL(c(x1)) = 4 + (2)x_1
POL(s(x1)) = 0
POL(G(x1, x2)) = (4)x_2
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
f(0) → true
f(1) → false
f(s(x)) → f(x)
if(true, s(x), s(y)) → s(x)
if(false, s(x), s(y)) → s(y)
g(x, c(y)) → c(g(x, y))
g(x, c(y)) → g(x, if(f(x), c(g(s(x), y)), c(y)))