R
↳Dependency Pair Analysis
+'(x, s(y)) -> +'(x, y)
+'(s(x), y) -> +'(x, y)
+'(x, +(y, z)) -> +'(+(x, y), z)
+'(x, +(y, z)) -> +'(x, y)
F(g(f(x))) -> F(h(s(0), x))
F(g(h(x, y))) -> F(h(s(x), y))
F(h(x, h(y, z))) -> F(h(+(x, y), z))
F(h(x, h(y, z))) -> +'(x, y)
R
↳DPs
→DP Problem 1
↳Argument Filtering and Ordering
→DP Problem 2
↳AFS
+'(x, +(y, z)) -> +'(x, y)
+'(x, +(y, z)) -> +'(+(x, y), z)
+'(s(x), y) -> +'(x, y)
+'(x, s(y)) -> +'(x, y)
+(x, 0) -> x
+(x, s(y)) -> s(+(x, y))
+(0, y) -> y
+(s(x), y) -> s(+(x, y))
+(x, +(y, z)) -> +(+(x, y), z)
f(g(f(x))) -> f(h(s(0), x))
f(g(h(x, y))) -> f(h(s(x), y))
f(h(x, h(y, z))) -> f(h(+(x, y), z))
+'(x, +(y, z)) -> +'(x, y)
+(x, 0) -> x
+(x, s(y)) -> s(+(x, y))
+(0, y) -> y
+(s(x), y) -> s(+(x, y))
+(x, +(y, z)) -> +(+(x, y), z)
POL(0) = 1 POL(s(x1)) = x1 POL(+(x1, x2)) = 1 + x1 + x2 POL(+'(x1, x2)) = 1 + x1 + x2
+'(x1, x2) -> +'(x1, x2)
+(x1, x2) -> +(x1, x2)
s(x1) -> s(x1)
R
↳DPs
→DP Problem 1
↳AFS
→DP Problem 3
↳Argument Filtering and Ordering
→DP Problem 2
↳AFS
+'(x, +(y, z)) -> +'(+(x, y), z)
+'(s(x), y) -> +'(x, y)
+'(x, s(y)) -> +'(x, y)
+(x, 0) -> x
+(x, s(y)) -> s(+(x, y))
+(0, y) -> y
+(s(x), y) -> s(+(x, y))
+(x, +(y, z)) -> +(+(x, y), z)
f(g(f(x))) -> f(h(s(0), x))
f(g(h(x, y))) -> f(h(s(x), y))
f(h(x, h(y, z))) -> f(h(+(x, y), z))
+'(s(x), y) -> +'(x, y)
+'(x, s(y)) -> +'(x, y)
+(x, 0) -> x
+(x, s(y)) -> s(+(x, y))
+(0, y) -> y
+(s(x), y) -> s(+(x, y))
+(x, +(y, z)) -> +(+(x, y), z)
POL(0) = 0 POL(s(x1)) = 1 + x1 POL(+(x1, x2)) = x1 + x2 POL(+'(x1, x2)) = x1 + x2
+'(x1, x2) -> +'(x1, x2)
s(x1) -> s(x1)
+(x1, x2) -> +(x1, x2)
R
↳DPs
→DP Problem 1
↳AFS
→DP Problem 3
↳AFS
...
→DP Problem 4
↳Argument Filtering and Ordering
→DP Problem 2
↳AFS
+'(x, +(y, z)) -> +'(+(x, y), z)
+(x, 0) -> x
+(x, s(y)) -> s(+(x, y))
+(0, y) -> y
+(s(x), y) -> s(+(x, y))
+(x, +(y, z)) -> +(+(x, y), z)
f(g(f(x))) -> f(h(s(0), x))
f(g(h(x, y))) -> f(h(s(x), y))
f(h(x, h(y, z))) -> f(h(+(x, y), z))
+'(x, +(y, z)) -> +'(+(x, y), z)
POL(+(x1, x2)) = 1 + x1 + x2
+'(x1, x2) -> x2
+(x1, x2) -> +(x1, x2)
R
↳DPs
→DP Problem 1
↳AFS
→DP Problem 3
↳AFS
...
→DP Problem 5
↳Dependency Graph
→DP Problem 2
↳AFS
+(x, 0) -> x
+(x, s(y)) -> s(+(x, y))
+(0, y) -> y
+(s(x), y) -> s(+(x, y))
+(x, +(y, z)) -> +(+(x, y), z)
f(g(f(x))) -> f(h(s(0), x))
f(g(h(x, y))) -> f(h(s(x), y))
f(h(x, h(y, z))) -> f(h(+(x, y), z))
R
↳DPs
→DP Problem 1
↳AFS
→DP Problem 2
↳Argument Filtering and Ordering
F(h(x, h(y, z))) -> F(h(+(x, y), z))
+(x, 0) -> x
+(x, s(y)) -> s(+(x, y))
+(0, y) -> y
+(s(x), y) -> s(+(x, y))
+(x, +(y, z)) -> +(+(x, y), z)
f(g(f(x))) -> f(h(s(0), x))
f(g(h(x, y))) -> f(h(s(x), y))
f(h(x, h(y, z))) -> f(h(+(x, y), z))
F(h(x, h(y, z))) -> F(h(+(x, y), z))
+(x, 0) -> x
+(x, s(y)) -> s(+(x, y))
+(0, y) -> y
+(s(x), y) -> s(+(x, y))
+(x, +(y, z)) -> +(+(x, y), z)
POL(0) = 1 POL(h(x1, x2)) = 1 + x1 + x2 POL(s(x1)) = x1 POL(F(x1)) = 1 + x1 POL(+(x1, x2)) = x1 + x2
F(x1) -> F(x1)
h(x1, x2) -> h(x1, x2)
+(x1, x2) -> +(x1, x2)
s(x1) -> s(x1)
R
↳DPs
→DP Problem 1
↳AFS
→DP Problem 2
↳AFS
→DP Problem 6
↳Dependency Graph
+(x, 0) -> x
+(x, s(y)) -> s(+(x, y))
+(0, y) -> y
+(s(x), y) -> s(+(x, y))
+(x, +(y, z)) -> +(+(x, y), z)
f(g(f(x))) -> f(h(s(0), x))
f(g(h(x, y))) -> f(h(s(x), y))
f(h(x, h(y, z))) -> f(h(+(x, y), z))