R
↳Dependency Pair Analysis
F(c(s(x), y)) -> F(c(x, s(y)))
G(c(x, s(y))) -> G(c(s(x), y))
G(s(f(x))) -> G(f(x))
R
↳DPs
→DP Problem 1
↳Argument Filtering and Ordering
→DP Problem 2
↳AFS
→DP Problem 3
↳FwdInst
F(c(s(x), y)) -> F(c(x, s(y)))
f(c(s(x), y)) -> f(c(x, s(y)))
g(c(x, s(y))) -> g(c(s(x), y))
g(s(f(x))) -> g(f(x))
F(c(s(x), y)) -> F(c(x, s(y)))
POL(s(x1)) = 1 + x1 POL(F(x1)) = x1
F(x1) -> F(x1)
c(x1, x2) -> x1
s(x1) -> s(x1)
R
↳DPs
→DP Problem 1
↳AFS
→DP Problem 4
↳Dependency Graph
→DP Problem 2
↳AFS
→DP Problem 3
↳FwdInst
f(c(s(x), y)) -> f(c(x, s(y)))
g(c(x, s(y))) -> g(c(s(x), y))
g(s(f(x))) -> g(f(x))
R
↳DPs
→DP Problem 1
↳AFS
→DP Problem 2
↳Argument Filtering and Ordering
→DP Problem 3
↳FwdInst
G(c(x, s(y))) -> G(c(s(x), y))
f(c(s(x), y)) -> f(c(x, s(y)))
g(c(x, s(y))) -> g(c(s(x), y))
g(s(f(x))) -> g(f(x))
G(c(x, s(y))) -> G(c(s(x), y))
POL(G(x1)) = x1 POL(s(x1)) = 1 + x1
G(x1) -> G(x1)
c(x1, x2) -> x2
s(x1) -> s(x1)
R
↳DPs
→DP Problem 1
↳AFS
→DP Problem 2
↳AFS
→DP Problem 5
↳Dependency Graph
→DP Problem 3
↳FwdInst
f(c(s(x), y)) -> f(c(x, s(y)))
g(c(x, s(y))) -> g(c(s(x), y))
g(s(f(x))) -> g(f(x))
R
↳DPs
→DP Problem 1
↳AFS
→DP Problem 2
↳AFS
→DP Problem 3
↳Forward Instantiation Transformation
G(s(f(x))) -> G(f(x))
f(c(s(x), y)) -> f(c(x, s(y)))
g(c(x, s(y))) -> g(c(s(x), y))
g(s(f(x))) -> g(f(x))
no new Dependency Pairs are created.
G(s(f(x))) -> G(f(x))