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
↳Inst
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
↳Inst
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
↳Argument Filtering and Ordering
→DP Problem 2
↳Inst
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
G(c(s(s(x'''')), s(y''''))) -> G(c(s(s(s(x''''))), y''''))
G(x1) -> G(x1)
c(x1, x2) -> x2
s(x1) -> s(x1)
R
↳DPs
→DP Problem 1
↳Inst
→DP Problem 3
↳Inst
...
→DP Problem 5
↳Dependency Graph
→DP Problem 2
↳Inst
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
↳Instantiation Transformation
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
one new Dependency Pair is created:
F(c(s(x), y)) -> F(c(x, s(y)))
F(c(s(x''), s(y''))) -> F(c(x'', s(s(y''))))
R
↳DPs
→DP Problem 1
↳Inst
→DP Problem 2
↳Inst
→DP Problem 6
↳Instantiation Transformation
F(c(s(x''), s(y''))) -> F(c(x'', s(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
one new Dependency Pair is created:
F(c(s(x''), s(y''))) -> F(c(x'', s(s(y''))))
F(c(s(x''''), s(s(y'''')))) -> F(c(x'''', s(s(s(y'''')))))
R
↳DPs
→DP Problem 1
↳Inst
→DP Problem 2
↳Inst
→DP Problem 6
↳Inst
...
→DP Problem 7
↳Argument Filtering and Ordering
F(c(s(x''''), s(s(y'''')))) -> F(c(x'''', s(s(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
F(c(s(x''''), s(s(y'''')))) -> F(c(x'''', s(s(s(y'''')))))
F(x1) -> F(x1)
c(x1, x2) -> x1
s(x1) -> s(x1)
R
↳DPs
→DP Problem 1
↳Inst
→DP Problem 2
↳Inst
→DP Problem 6
↳Inst
...
→DP Problem 8
↳Dependency Graph
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