*** 1 Progress [(O(1),O(n^1))] ***
Considered Problem:
Strict DP Rules:
Strict TRS Rules:
f(f(x)) -> f(c(f(x)))
f(f(x)) -> f(d(f(x)))
g(c(x)) -> x
g(c(1())) -> g(d(h(0())))
g(c(h(0()))) -> g(d(1()))
g(d(x)) -> x
g(h(x)) -> g(x)
Weak DP Rules:
Weak TRS Rules:
Signature:
{f/1,g/1} / {0/0,1/0,c/1,d/1,h/1}
Obligation:
Innermost
basic terms: {f,g}/{0,1,c,d,h}
Applied Processor:
Bounds {initialAutomaton = minimal, enrichment = match}
Proof:
The problem is match-bounded by 1.
The enriched problem is compatible with follwoing automaton.
0_0() -> 1
0_0() -> 2
0_1() -> 5
1_0() -> 1
1_0() -> 2
1_1() -> 1
1_1() -> 4
c_0(2) -> 1
c_0(2) -> 2
d_0(2) -> 1
d_0(2) -> 2
d_1(4) -> 3
f_0(2) -> 1
g_0(2) -> 1
g_1(2) -> 1
g_1(3) -> 1
h_0(2) -> 1
h_0(2) -> 2
h_1(5) -> 1
h_1(5) -> 4
2 -> 1
4 -> 1
*** 1.1 Progress [(O(1),O(1))] ***
Considered Problem:
Strict DP Rules:
Strict TRS Rules:
Weak DP Rules:
Weak TRS Rules:
f(f(x)) -> f(c(f(x)))
f(f(x)) -> f(d(f(x)))
g(c(x)) -> x
g(c(1())) -> g(d(h(0())))
g(c(h(0()))) -> g(d(1()))
g(d(x)) -> x
g(h(x)) -> g(x)
Signature:
{f/1,g/1} / {0/0,1/0,c/1,d/1,h/1}
Obligation:
Innermost
basic terms: {f,g}/{0,1,c,d,h}
Applied Processor:
EmptyProcessor
Proof:
The problem is already closed. The intended complexity is O(1).