R
↳Dependency Pair Analysis
F(0, 1, g(x, y), z) -> F(g(x, y), g(x, y), g(x, y), h(x))
F(0, 1, g(x, y), z) -> H(x)
H(g(x, y)) -> H(x)
R
↳DPs
→DP Problem 1
↳Forward Instantiation Transformation
H(g(x, y)) -> H(x)
f(0, 1, g(x, y), z) -> f(g(x, y), g(x, y), g(x, y), h(x))
g(0, 1) -> 0
g(0, 1) -> 1
h(g(x, y)) -> h(x)
innermost
one new Dependency Pair is created:
H(g(x, y)) -> H(x)
H(g(g(x'', y''), y)) -> H(g(x'', y''))
R
↳DPs
→DP Problem 1
↳FwdInst
→DP Problem 2
↳Forward Instantiation Transformation
H(g(g(x'', y''), y)) -> H(g(x'', y''))
f(0, 1, g(x, y), z) -> f(g(x, y), g(x, y), g(x, y), h(x))
g(0, 1) -> 0
g(0, 1) -> 1
h(g(x, y)) -> h(x)
innermost
one new Dependency Pair is created:
H(g(g(x'', y''), y)) -> H(g(x'', y''))
H(g(g(g(x'''', y''''), y''0), y)) -> H(g(g(x'''', y''''), y''0))
R
↳DPs
→DP Problem 1
↳FwdInst
→DP Problem 2
↳FwdInst
...
→DP Problem 3
↳Argument Filtering and Ordering
H(g(g(g(x'''', y''''), y''0), y)) -> H(g(g(x'''', y''''), y''0))
f(0, 1, g(x, y), z) -> f(g(x, y), g(x, y), g(x, y), h(x))
g(0, 1) -> 0
g(0, 1) -> 1
h(g(x, y)) -> h(x)
innermost
H(g(g(g(x'''', y''''), y''0), y)) -> H(g(g(x'''', y''''), y''0))
g(0, 1) -> 0
g(0, 1) -> 1
H(x1) -> H(x1)
g(x1, x2) -> g(x1, x2)
R
↳DPs
→DP Problem 1
↳FwdInst
→DP Problem 2
↳FwdInst
...
→DP Problem 4
↳Dependency Graph
f(0, 1, g(x, y), z) -> f(g(x, y), g(x, y), g(x, y), h(x))
g(0, 1) -> 0
g(0, 1) -> 1
h(g(x, y)) -> h(x)
innermost