R
↳Dependency Pair Analysis
F(s(X)) -> F(X)
G(cons(0, Y)) -> G(Y)
H(cons(X, Y)) -> H(g(cons(X, Y)))
H(cons(X, Y)) -> G(cons(X, Y))
R
↳DPs
→DP Problem 1
↳Argument Filtering and Ordering
→DP Problem 2
↳AFS
→DP Problem 3
↳FwdInst
F(s(X)) -> F(X)
f(s(X)) -> f(X)
g(cons(0, Y)) -> g(Y)
g(cons(s(X), Y)) -> s(X)
h(cons(X, Y)) -> h(g(cons(X, Y)))
innermost
F(s(X)) -> F(X)
POL(s(x1)) = 1 + x1 POL(F(x1)) = x1
F(x1) -> F(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(s(X)) -> f(X)
g(cons(0, Y)) -> g(Y)
g(cons(s(X), Y)) -> s(X)
h(cons(X, Y)) -> h(g(cons(X, Y)))
innermost
R
↳DPs
→DP Problem 1
↳AFS
→DP Problem 2
↳Argument Filtering and Ordering
→DP Problem 3
↳FwdInst
G(cons(0, Y)) -> G(Y)
f(s(X)) -> f(X)
g(cons(0, Y)) -> g(Y)
g(cons(s(X), Y)) -> s(X)
h(cons(X, Y)) -> h(g(cons(X, Y)))
innermost
G(cons(0, Y)) -> G(Y)
POL(0) = 0 POL(G(x1)) = x1 POL(cons(x1, x2)) = 1 + x1 + x2
G(x1) -> G(x1)
cons(x1, x2) -> cons(x1, x2)
R
↳DPs
→DP Problem 1
↳AFS
→DP Problem 2
↳AFS
→DP Problem 5
↳Dependency Graph
→DP Problem 3
↳FwdInst
f(s(X)) -> f(X)
g(cons(0, Y)) -> g(Y)
g(cons(s(X), Y)) -> s(X)
h(cons(X, Y)) -> h(g(cons(X, Y)))
innermost
R
↳DPs
→DP Problem 1
↳AFS
→DP Problem 2
↳AFS
→DP Problem 3
↳Forward Instantiation Transformation
H(cons(X, Y)) -> H(g(cons(X, Y)))
f(s(X)) -> f(X)
g(cons(0, Y)) -> g(Y)
g(cons(s(X), Y)) -> s(X)
h(cons(X, Y)) -> h(g(cons(X, Y)))
innermost
no new Dependency Pairs are created.
H(cons(X, Y)) -> H(g(cons(X, Y)))