R
↳Dependency Pair Analysis
ACTIVE(f(g(X), Y)) -> F(X, f(g(X), Y))
ACTIVE(f(X1, X2)) -> F(active(X1), X2)
ACTIVE(f(X1, X2)) -> ACTIVE(X1)
ACTIVE(g(X)) -> G(active(X))
ACTIVE(g(X)) -> ACTIVE(X)
F(mark(X1), X2) -> F(X1, X2)
F(ok(X1), ok(X2)) -> F(X1, X2)
G(mark(X)) -> G(X)
G(ok(X)) -> G(X)
PROPER(f(X1, X2)) -> F(proper(X1), proper(X2))
PROPER(f(X1, X2)) -> PROPER(X1)
PROPER(f(X1, X2)) -> PROPER(X2)
PROPER(g(X)) -> G(proper(X))
PROPER(g(X)) -> PROPER(X)
TOP(mark(X)) -> TOP(proper(X))
TOP(mark(X)) -> PROPER(X)
TOP(ok(X)) -> TOP(active(X))
TOP(ok(X)) -> ACTIVE(X)
R
↳DPs
→DP Problem 1
↳Argument Filtering and Ordering
→DP Problem 2
↳AFS
→DP Problem 3
↳AFS
→DP Problem 4
↳AFS
→DP Problem 5
↳AFS
F(ok(X1), ok(X2)) -> F(X1, X2)
F(mark(X1), X2) -> F(X1, X2)
active(f(g(X), Y)) -> mark(f(X, f(g(X), Y)))
active(f(X1, X2)) -> f(active(X1), X2)
active(g(X)) -> g(active(X))
f(mark(X1), X2) -> mark(f(X1, X2))
f(ok(X1), ok(X2)) -> ok(f(X1, X2))
g(mark(X)) -> mark(g(X))
g(ok(X)) -> ok(g(X))
proper(f(X1, X2)) -> f(proper(X1), proper(X2))
proper(g(X)) -> g(proper(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
F(ok(X1), ok(X2)) -> F(X1, X2)
F(mark(X1), X2) -> F(X1, X2)
trivial
F(x1, x2) -> F(x1, x2)
ok(x1) -> ok(x1)
mark(x1) -> mark(x1)
R
↳DPs
→DP Problem 1
↳AFS
→DP Problem 6
↳Dependency Graph
→DP Problem 2
↳AFS
→DP Problem 3
↳AFS
→DP Problem 4
↳AFS
→DP Problem 5
↳AFS
active(f(g(X), Y)) -> mark(f(X, f(g(X), Y)))
active(f(X1, X2)) -> f(active(X1), X2)
active(g(X)) -> g(active(X))
f(mark(X1), X2) -> mark(f(X1, X2))
f(ok(X1), ok(X2)) -> ok(f(X1, X2))
g(mark(X)) -> mark(g(X))
g(ok(X)) -> ok(g(X))
proper(f(X1, X2)) -> f(proper(X1), proper(X2))
proper(g(X)) -> g(proper(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
R
↳DPs
→DP Problem 1
↳AFS
→DP Problem 2
↳Argument Filtering and Ordering
→DP Problem 3
↳AFS
→DP Problem 4
↳AFS
→DP Problem 5
↳AFS
G(ok(X)) -> G(X)
G(mark(X)) -> G(X)
active(f(g(X), Y)) -> mark(f(X, f(g(X), Y)))
active(f(X1, X2)) -> f(active(X1), X2)
active(g(X)) -> g(active(X))
f(mark(X1), X2) -> mark(f(X1, X2))
f(ok(X1), ok(X2)) -> ok(f(X1, X2))
g(mark(X)) -> mark(g(X))
g(ok(X)) -> ok(g(X))
proper(f(X1, X2)) -> f(proper(X1), proper(X2))
proper(g(X)) -> g(proper(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
G(ok(X)) -> G(X)
G(mark(X)) -> G(X)
trivial
G(x1) -> G(x1)
ok(x1) -> ok(x1)
mark(x1) -> mark(x1)
R
↳DPs
→DP Problem 1
↳AFS
→DP Problem 2
↳AFS
→DP Problem 7
↳Dependency Graph
→DP Problem 3
↳AFS
→DP Problem 4
↳AFS
→DP Problem 5
↳AFS
active(f(g(X), Y)) -> mark(f(X, f(g(X), Y)))
active(f(X1, X2)) -> f(active(X1), X2)
active(g(X)) -> g(active(X))
f(mark(X1), X2) -> mark(f(X1, X2))
f(ok(X1), ok(X2)) -> ok(f(X1, X2))
g(mark(X)) -> mark(g(X))
g(ok(X)) -> ok(g(X))
proper(f(X1, X2)) -> f(proper(X1), proper(X2))
proper(g(X)) -> g(proper(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
R
↳DPs
→DP Problem 1
↳AFS
→DP Problem 2
↳AFS
→DP Problem 3
↳Argument Filtering and Ordering
→DP Problem 4
↳AFS
→DP Problem 5
↳AFS
ACTIVE(g(X)) -> ACTIVE(X)
ACTIVE(f(X1, X2)) -> ACTIVE(X1)
active(f(g(X), Y)) -> mark(f(X, f(g(X), Y)))
active(f(X1, X2)) -> f(active(X1), X2)
active(g(X)) -> g(active(X))
f(mark(X1), X2) -> mark(f(X1, X2))
f(ok(X1), ok(X2)) -> ok(f(X1, X2))
g(mark(X)) -> mark(g(X))
g(ok(X)) -> ok(g(X))
proper(f(X1, X2)) -> f(proper(X1), proper(X2))
proper(g(X)) -> g(proper(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
ACTIVE(g(X)) -> ACTIVE(X)
ACTIVE(f(X1, X2)) -> ACTIVE(X1)
trivial
ACTIVE(x1) -> ACTIVE(x1)
g(x1) -> g(x1)
f(x1, x2) -> f(x1, x2)
R
↳DPs
→DP Problem 1
↳AFS
→DP Problem 2
↳AFS
→DP Problem 3
↳AFS
→DP Problem 8
↳Dependency Graph
→DP Problem 4
↳AFS
→DP Problem 5
↳AFS
active(f(g(X), Y)) -> mark(f(X, f(g(X), Y)))
active(f(X1, X2)) -> f(active(X1), X2)
active(g(X)) -> g(active(X))
f(mark(X1), X2) -> mark(f(X1, X2))
f(ok(X1), ok(X2)) -> ok(f(X1, X2))
g(mark(X)) -> mark(g(X))
g(ok(X)) -> ok(g(X))
proper(f(X1, X2)) -> f(proper(X1), proper(X2))
proper(g(X)) -> g(proper(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
R
↳DPs
→DP Problem 1
↳AFS
→DP Problem 2
↳AFS
→DP Problem 3
↳AFS
→DP Problem 4
↳Argument Filtering and Ordering
→DP Problem 5
↳AFS
PROPER(g(X)) -> PROPER(X)
PROPER(f(X1, X2)) -> PROPER(X2)
PROPER(f(X1, X2)) -> PROPER(X1)
active(f(g(X), Y)) -> mark(f(X, f(g(X), Y)))
active(f(X1, X2)) -> f(active(X1), X2)
active(g(X)) -> g(active(X))
f(mark(X1), X2) -> mark(f(X1, X2))
f(ok(X1), ok(X2)) -> ok(f(X1, X2))
g(mark(X)) -> mark(g(X))
g(ok(X)) -> ok(g(X))
proper(f(X1, X2)) -> f(proper(X1), proper(X2))
proper(g(X)) -> g(proper(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
PROPER(g(X)) -> PROPER(X)
PROPER(f(X1, X2)) -> PROPER(X2)
PROPER(f(X1, X2)) -> PROPER(X1)
trivial
PROPER(x1) -> PROPER(x1)
f(x1, x2) -> f(x1, x2)
g(x1) -> g(x1)
R
↳DPs
→DP Problem 1
↳AFS
→DP Problem 2
↳AFS
→DP Problem 3
↳AFS
→DP Problem 4
↳AFS
→DP Problem 9
↳Dependency Graph
→DP Problem 5
↳AFS
active(f(g(X), Y)) -> mark(f(X, f(g(X), Y)))
active(f(X1, X2)) -> f(active(X1), X2)
active(g(X)) -> g(active(X))
f(mark(X1), X2) -> mark(f(X1, X2))
f(ok(X1), ok(X2)) -> ok(f(X1, X2))
g(mark(X)) -> mark(g(X))
g(ok(X)) -> ok(g(X))
proper(f(X1, X2)) -> f(proper(X1), proper(X2))
proper(g(X)) -> g(proper(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
R
↳DPs
→DP Problem 1
↳AFS
→DP Problem 2
↳AFS
→DP Problem 3
↳AFS
→DP Problem 4
↳AFS
→DP Problem 5
↳Argument Filtering and Ordering
TOP(ok(X)) -> TOP(active(X))
TOP(mark(X)) -> TOP(proper(X))
active(f(g(X), Y)) -> mark(f(X, f(g(X), Y)))
active(f(X1, X2)) -> f(active(X1), X2)
active(g(X)) -> g(active(X))
f(mark(X1), X2) -> mark(f(X1, X2))
f(ok(X1), ok(X2)) -> ok(f(X1, X2))
g(mark(X)) -> mark(g(X))
g(ok(X)) -> ok(g(X))
proper(f(X1, X2)) -> f(proper(X1), proper(X2))
proper(g(X)) -> g(proper(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
TOP(mark(X)) -> TOP(proper(X))
proper(f(X1, X2)) -> f(proper(X1), proper(X2))
proper(g(X)) -> g(proper(X))
active(f(g(X), Y)) -> mark(f(X, f(g(X), Y)))
active(f(X1, X2)) -> f(active(X1), X2)
active(g(X)) -> g(active(X))
f(mark(X1), X2) -> mark(f(X1, X2))
f(ok(X1), ok(X2)) -> ok(f(X1, X2))
g(mark(X)) -> mark(g(X))
g(ok(X)) -> ok(g(X))
{active, mark, ok} > proper
TOP(x1) -> TOP(x1)
mark(x1) -> mark(x1)
proper(x1) -> proper(x1)
ok(x1) -> ok(x1)
active(x1) -> active(x1)
f(x1, x2) -> x1
g(x1) -> x1
R
↳DPs
→DP Problem 1
↳AFS
→DP Problem 2
↳AFS
→DP Problem 3
↳AFS
→DP Problem 4
↳AFS
→DP Problem 5
↳AFS
→DP Problem 10
↳Argument Filtering and Ordering
TOP(ok(X)) -> TOP(active(X))
active(f(g(X), Y)) -> mark(f(X, f(g(X), Y)))
active(f(X1, X2)) -> f(active(X1), X2)
active(g(X)) -> g(active(X))
f(mark(X1), X2) -> mark(f(X1, X2))
f(ok(X1), ok(X2)) -> ok(f(X1, X2))
g(mark(X)) -> mark(g(X))
g(ok(X)) -> ok(g(X))
proper(f(X1, X2)) -> f(proper(X1), proper(X2))
proper(g(X)) -> g(proper(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
TOP(ok(X)) -> TOP(active(X))
active(f(g(X), Y)) -> mark(f(X, f(g(X), Y)))
active(f(X1, X2)) -> f(active(X1), X2)
active(g(X)) -> g(active(X))
f(mark(X1), X2) -> mark(f(X1, X2))
f(ok(X1), ok(X2)) -> ok(f(X1, X2))
g(mark(X)) -> mark(g(X))
g(ok(X)) -> ok(g(X))
ok > {active, mark}
TOP(x1) -> TOP(x1)
ok(x1) -> ok(x1)
active(x1) -> active(x1)
f(x1, x2) -> x1
g(x1) -> x1
mark(x1) -> mark(x1)
R
↳DPs
→DP Problem 1
↳AFS
→DP Problem 2
↳AFS
→DP Problem 3
↳AFS
→DP Problem 4
↳AFS
→DP Problem 5
↳AFS
→DP Problem 10
↳AFS
...
→DP Problem 11
↳Dependency Graph
active(f(g(X), Y)) -> mark(f(X, f(g(X), Y)))
active(f(X1, X2)) -> f(active(X1), X2)
active(g(X)) -> g(active(X))
f(mark(X1), X2) -> mark(f(X1, X2))
f(ok(X1), ok(X2)) -> ok(f(X1, X2))
g(mark(X)) -> mark(g(X))
g(ok(X)) -> ok(g(X))
proper(f(X1, X2)) -> f(proper(X1), proper(X2))
proper(g(X)) -> g(proper(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))