f(0) → true
f(1) → false
f(s(x)) → f(x)
if(true, x, y) → x
if(false, x, y) → y
g(s(x), s(y)) → if(f(x), s(x), s(y))
g(x, c(y)) → g(x, g(s(c(y)), y))
↳ QTRS
↳ DependencyPairsProof
f(0) → true
f(1) → false
f(s(x)) → f(x)
if(true, x, y) → x
if(false, x, y) → y
g(s(x), s(y)) → if(f(x), s(x), s(y))
g(x, c(y)) → g(x, g(s(c(y)), y))
G(x, c(y)) → G(x, g(s(c(y)), y))
F(s(x)) → F(x)
G(s(x), s(y)) → IF(f(x), s(x), s(y))
G(x, c(y)) → G(s(c(y)), y)
G(s(x), s(y)) → F(x)
f(0) → true
f(1) → false
f(s(x)) → f(x)
if(true, x, y) → x
if(false, x, y) → y
g(s(x), s(y)) → if(f(x), s(x), s(y))
g(x, c(y)) → g(x, g(s(c(y)), y))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
G(x, c(y)) → G(x, g(s(c(y)), y))
F(s(x)) → F(x)
G(s(x), s(y)) → IF(f(x), s(x), s(y))
G(x, c(y)) → G(s(c(y)), y)
G(s(x), s(y)) → F(x)
f(0) → true
f(1) → false
f(s(x)) → f(x)
if(true, x, y) → x
if(false, x, y) → y
g(s(x), s(y)) → if(f(x), s(x), s(y))
g(x, c(y)) → g(x, g(s(c(y)), 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, x, y) → x
if(false, x, y) → y
g(s(x), s(y)) → if(f(x), s(x), s(y))
g(x, c(y)) → g(x, g(s(c(y)), 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 4.
POL(s(x1)) = 1 + (4)x_1
POL(F(x1)) = (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, x, y) → x
if(false, x, y) → y
g(s(x), s(y)) → if(f(x), s(x), s(y))
g(x, c(y)) → g(x, g(s(c(y)), y))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
G(x, c(y)) → G(x, g(s(c(y)), y))
G(x, c(y)) → G(s(c(y)), y)
f(0) → true
f(1) → false
f(s(x)) → f(x)
if(true, x, y) → x
if(false, x, y) → y
g(s(x), s(y)) → if(f(x), s(x), s(y))
g(x, c(y)) → g(x, g(s(c(y)), 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, g(s(c(y)), y))
G(x, c(y)) → G(s(c(y)), y)
The value of delta used in the strict ordering is 5/8.
POL(c(x1)) = 1/4 + (4)x_1
POL(f(x1)) = 3
POL(if(x1, x2, x3)) = x_2 + (2)x_3
POL(g(x1, x2)) = (3/2)x_1 + (2)x_2
POL(true) = 4
POL(false) = 3/2
POL(s(x1)) = (1/4)x_1
POL(G(x1, x2)) = (4)x_1 + (4)x_2
POL(0) = 7/2
POL(1) = 4
if(true, x, y) → x
if(false, x, y) → y
g(s(x), s(y)) → if(f(x), s(x), s(y))
g(x, c(y)) → g(x, g(s(c(y)), y))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
f(0) → true
f(1) → false
f(s(x)) → f(x)
if(true, x, y) → x
if(false, x, y) → y
g(s(x), s(y)) → if(f(x), s(x), s(y))
g(x, c(y)) → g(x, g(s(c(y)), y))