*** 1 Progress [(O(1),O(n^1))] ***
Considered Problem:
Strict DP Rules:
Strict TRS Rules:
active(f(X)) -> f(active(X))
active(f(f(a()))) -> mark(c(f(g(f(a())))))
active(g(X)) -> g(active(X))
c(ok(X)) -> ok(c(X))
f(mark(X)) -> mark(f(X))
f(ok(X)) -> ok(f(X))
g(mark(X)) -> mark(g(X))
g(ok(X)) -> ok(g(X))
proper(a()) -> ok(a())
proper(c(X)) -> c(proper(X))
proper(f(X)) -> f(proper(X))
proper(g(X)) -> g(proper(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
Weak DP Rules:
Weak TRS Rules:
Signature:
{active/1,c/1,f/1,g/1,proper/1,top/1} / {a/0,mark/1,ok/1}
Obligation:
Innermost
basic terms: {active,c,f,g,proper,top}/{a,mark,ok}
Applied Processor:
Bounds {initialAutomaton = perSymbol, enrichment = match}
Proof:
The problem is match-bounded by 2.
The enriched problem is compatible with follwoing automaton.
a_0() -> 1
a_1() -> 13
active_0(1) -> 2
active_0(6) -> 2
active_0(7) -> 2
active_1(1) -> 14
active_1(6) -> 14
active_1(7) -> 14
active_2(13) -> 15
c_0(1) -> 3
c_0(6) -> 3
c_0(7) -> 3
c_1(1) -> 10
c_1(6) -> 10
c_1(7) -> 10
f_0(1) -> 4
f_0(6) -> 4
f_0(7) -> 4
f_1(1) -> 11
f_1(6) -> 11
f_1(7) -> 11
g_0(1) -> 5
g_0(6) -> 5
g_0(7) -> 5
g_1(1) -> 12
g_1(6) -> 12
g_1(7) -> 12
mark_0(1) -> 6
mark_0(6) -> 6
mark_0(7) -> 6
mark_1(11) -> 4
mark_1(11) -> 11
mark_1(12) -> 5
mark_1(12) -> 12
ok_0(1) -> 7
ok_0(6) -> 7
ok_0(7) -> 7
ok_1(10) -> 3
ok_1(10) -> 10
ok_1(11) -> 4
ok_1(11) -> 11
ok_1(12) -> 5
ok_1(12) -> 12
ok_1(13) -> 8
ok_1(13) -> 14
proper_0(1) -> 8
proper_0(6) -> 8
proper_0(7) -> 8
proper_1(1) -> 14
proper_1(6) -> 14
proper_1(7) -> 14
top_0(1) -> 9
top_0(6) -> 9
top_0(7) -> 9
top_1(14) -> 9
top_2(15) -> 9
*** 1.1 Progress [(O(1),O(1))] ***
Considered Problem:
Strict DP Rules:
Strict TRS Rules:
Weak DP Rules:
Weak TRS Rules:
active(f(X)) -> f(active(X))
active(f(f(a()))) -> mark(c(f(g(f(a())))))
active(g(X)) -> g(active(X))
c(ok(X)) -> ok(c(X))
f(mark(X)) -> mark(f(X))
f(ok(X)) -> ok(f(X))
g(mark(X)) -> mark(g(X))
g(ok(X)) -> ok(g(X))
proper(a()) -> ok(a())
proper(c(X)) -> c(proper(X))
proper(f(X)) -> f(proper(X))
proper(g(X)) -> g(proper(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
Signature:
{active/1,c/1,f/1,g/1,proper/1,top/1} / {a/0,mark/1,ok/1}
Obligation:
Innermost
basic terms: {active,c,f,g,proper,top}/{a,mark,ok}
Applied Processor:
EmptyProcessor
Proof:
The problem is already closed. The intended complexity is O(1).