R
↳Dependency Pair Analysis
F(c(s(x), y)) -> F(c(x, s(y)))
F(c(s(x), s(y))) -> G(c(x, y))
G(c(x, s(y))) -> G(c(s(x), y))
G(c(s(x), s(y))) -> F(c(x, y))
R
↳DPs
→DP Problem 1
↳Polynomial Ordering
G(c(s(x), s(y))) -> F(c(x, y))
G(c(x, s(y))) -> G(c(s(x), y))
F(c(s(x), s(y))) -> G(c(x, y))
F(c(s(x), y)) -> F(c(x, s(y)))
f(c(s(x), y)) -> f(c(x, s(y)))
f(c(s(x), s(y))) -> g(c(x, y))
g(c(x, s(y))) -> g(c(s(x), y))
g(c(s(x), s(y))) -> f(c(x, y))
G(c(s(x), s(y))) -> F(c(x, y))
F(c(s(x), s(y))) -> G(c(x, y))
f(c(s(x), y)) -> f(c(x, s(y)))
f(c(s(x), s(y))) -> g(c(x, y))
g(c(x, s(y))) -> g(c(s(x), y))
g(c(s(x), s(y))) -> f(c(x, y))
POL(c(x1, x2)) = x1 + x2 POL(g(x1)) = 0 POL(G(x1)) = x1 POL(s(x1)) = 1 + x1 POL(f(x1)) = 0 POL(F(x1)) = x1
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Dependency Graph
G(c(x, s(y))) -> G(c(s(x), y))
F(c(s(x), y)) -> F(c(x, s(y)))
f(c(s(x), y)) -> f(c(x, s(y)))
f(c(s(x), s(y))) -> g(c(x, y))
g(c(x, s(y))) -> g(c(s(x), y))
g(c(s(x), s(y))) -> f(c(x, y))
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳DGraph
...
→DP Problem 3
↳Polynomial Ordering
G(c(x, s(y))) -> G(c(s(x), y))
f(c(s(x), y)) -> f(c(x, s(y)))
f(c(s(x), s(y))) -> g(c(x, y))
g(c(x, s(y))) -> g(c(s(x), y))
g(c(s(x), s(y))) -> f(c(x, y))
G(c(x, s(y))) -> G(c(s(x), y))
f(c(s(x), y)) -> f(c(x, s(y)))
f(c(s(x), s(y))) -> g(c(x, y))
g(c(x, s(y))) -> g(c(s(x), y))
g(c(s(x), s(y))) -> f(c(x, y))
POL(c(x1, x2)) = x2 POL(g(x1)) = 0 POL(G(x1)) = x1 POL(s(x1)) = 1 + x1 POL(f(x1)) = 0
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳DGraph
...
→DP Problem 5
↳Dependency Graph
f(c(s(x), y)) -> f(c(x, s(y)))
f(c(s(x), s(y))) -> g(c(x, y))
g(c(x, s(y))) -> g(c(s(x), y))
g(c(s(x), s(y))) -> f(c(x, y))
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳DGraph
...
→DP Problem 4
↳Polynomial Ordering
F(c(s(x), y)) -> F(c(x, s(y)))
f(c(s(x), y)) -> f(c(x, s(y)))
f(c(s(x), s(y))) -> g(c(x, y))
g(c(x, s(y))) -> g(c(s(x), y))
g(c(s(x), s(y))) -> f(c(x, y))
F(c(s(x), y)) -> F(c(x, s(y)))
f(c(s(x), y)) -> f(c(x, s(y)))
f(c(s(x), s(y))) -> g(c(x, y))
g(c(x, s(y))) -> g(c(s(x), y))
g(c(s(x), s(y))) -> f(c(x, y))
POL(c(x1, x2)) = x1 POL(g(x1)) = 0 POL(s(x1)) = 1 + x1 POL(f(x1)) = 0 POL(F(x1)) = x1