R
↳Dependency Pair Analysis
F(s(x)) -> F(x)
G(s(0)) -> G(f(s(0)))
G(s(0)) -> F(s(0))
R
↳DPs
→DP Problem 1
↳Argument Filtering and Ordering
→DP Problem 2
↳FwdInst
F(s(x)) -> F(x)
f(f(x)) -> f(x)
f(s(x)) -> f(x)
g(s(0)) -> g(f(s(0)))
F(s(x)) -> F(x)
f(f(x)) -> f(x)
f(s(x)) -> f(x)
g(s(0)) -> g(f(s(0)))
POL(0) = 0 POL(g(x1)) = 1 + x1 POL(s(x1)) = 1 + x1 POL(F(x1)) = 1 + x1 POL(f(x1)) = x1
F(x1) -> F(x1)
s(x1) -> s(x1)
f(x1) -> f(x1)
g(x1) -> g(x1)
R
↳DPs
→DP Problem 1
↳AFS
→DP Problem 3
↳Dependency Graph
→DP Problem 2
↳FwdInst
f(f(x)) -> f(x)
f(s(x)) -> f(x)
g(s(0)) -> g(f(s(0)))
R
↳DPs
→DP Problem 1
↳AFS
→DP Problem 2
↳Forward Instantiation Transformation
G(s(0)) -> G(f(s(0)))
f(f(x)) -> f(x)
f(s(x)) -> f(x)
g(s(0)) -> g(f(s(0)))
no new Dependency Pairs are created.
G(s(0)) -> G(f(s(0)))