R
↳Dependency Pair Analysis
G(c(x, s(y))) -> G(c(s(x), y))
F(c(s(x), y)) -> F(c(x, s(y)))
F(f(x)) -> F(d(f(x)))
R
↳DPs
→DP Problem 1
↳Instantiation Transformation
→DP Problem 2
↳Remaining
G(c(x, s(y))) -> G(c(s(x), y))
g(c(x, s(y))) -> g(c(s(x), y))
f(c(s(x), y)) -> f(c(x, s(y)))
f(f(x)) -> f(d(f(x)))
f(x) -> x
one new Dependency Pair is created:
G(c(x, s(y))) -> G(c(s(x), y))
G(c(s(x''), s(y''))) -> G(c(s(s(x'')), y''))
R
↳DPs
→DP Problem 1
↳Inst
→DP Problem 3
↳Instantiation Transformation
→DP Problem 2
↳Remaining
G(c(s(x''), s(y''))) -> G(c(s(s(x'')), y''))
g(c(x, s(y))) -> g(c(s(x), y))
f(c(s(x), y)) -> f(c(x, s(y)))
f(f(x)) -> f(d(f(x)))
f(x) -> x
one new Dependency Pair is created:
G(c(s(x''), s(y''))) -> G(c(s(s(x'')), y''))
G(c(s(s(x'''')), s(y''''))) -> G(c(s(s(s(x''''))), y''''))
R
↳DPs
→DP Problem 1
↳Inst
→DP Problem 3
↳Inst
...
→DP Problem 4
↳Instantiation Transformation
→DP Problem 2
↳Remaining
G(c(s(s(x'''')), s(y''''))) -> G(c(s(s(s(x''''))), y''''))
g(c(x, s(y))) -> g(c(s(x), y))
f(c(s(x), y)) -> f(c(x, s(y)))
f(f(x)) -> f(d(f(x)))
f(x) -> x
one new Dependency Pair is created:
G(c(s(s(x'''')), s(y''''))) -> G(c(s(s(s(x''''))), y''''))
G(c(s(s(s(x''''''))), s(y''''''))) -> G(c(s(s(s(s(x'''''')))), y''''''))
R
↳DPs
→DP Problem 1
↳Inst
→DP Problem 3
↳Inst
...
→DP Problem 5
↳Instantiation Transformation
→DP Problem 2
↳Remaining
G(c(s(s(s(x''''''))), s(y''''''))) -> G(c(s(s(s(s(x'''''')))), y''''''))
g(c(x, s(y))) -> g(c(s(x), y))
f(c(s(x), y)) -> f(c(x, s(y)))
f(f(x)) -> f(d(f(x)))
f(x) -> x
one new Dependency Pair is created:
G(c(s(s(s(x''''''))), s(y''''''))) -> G(c(s(s(s(s(x'''''')))), y''''''))
G(c(s(s(s(s(x'''''''')))), s(y''''''''))) -> G(c(s(s(s(s(s(x''''''''))))), y''''''''))
R
↳DPs
→DP Problem 1
↳Inst
→DP Problem 3
↳Inst
...
→DP Problem 6
↳Instantiation Transformation
→DP Problem 2
↳Remaining
G(c(s(s(s(s(x'''''''')))), s(y''''''''))) -> G(c(s(s(s(s(s(x''''''''))))), y''''''''))
g(c(x, s(y))) -> g(c(s(x), y))
f(c(s(x), y)) -> f(c(x, s(y)))
f(f(x)) -> f(d(f(x)))
f(x) -> x
one new Dependency Pair is created:
G(c(s(s(s(s(x'''''''')))), s(y''''''''))) -> G(c(s(s(s(s(s(x''''''''))))), y''''''''))
G(c(s(s(s(s(s(x''''''''''))))), s(y''''''''''))) -> G(c(s(s(s(s(s(s(x'''''''''')))))), y''''''''''))
R
↳DPs
→DP Problem 1
↳Inst
→DP Problem 2
↳Remaining Obligation(s)
G(c(s(s(s(s(s(x''''''''''))))), s(y''''''''''))) -> G(c(s(s(s(s(s(s(x'''''''''')))))), y''''''''''))
g(c(x, s(y))) -> g(c(s(x), y))
f(c(s(x), y)) -> f(c(x, s(y)))
f(f(x)) -> f(d(f(x)))
f(x) -> x
F(c(s(x), y)) -> F(c(x, s(y)))
g(c(x, s(y))) -> g(c(s(x), y))
f(c(s(x), y)) -> f(c(x, s(y)))
f(f(x)) -> f(d(f(x)))
f(x) -> x
R
↳DPs
→DP Problem 1
↳Inst
→DP Problem 2
↳Remaining Obligation(s)
G(c(s(s(s(s(s(x''''''''''))))), s(y''''''''''))) -> G(c(s(s(s(s(s(s(x'''''''''')))))), y''''''''''))
g(c(x, s(y))) -> g(c(s(x), y))
f(c(s(x), y)) -> f(c(x, s(y)))
f(f(x)) -> f(d(f(x)))
f(x) -> x
F(c(s(x), y)) -> F(c(x, s(y)))
g(c(x, s(y))) -> g(c(s(x), y))
f(c(s(x), y)) -> f(c(x, s(y)))
f(f(x)) -> f(d(f(x)))
f(x) -> x