*** 1 Progress [(O(1),O(n^1))] ***
Considered Problem:
Strict DP Rules:
Strict TRS Rules:
f(a()) -> g(h(a()))
h(g(x)) -> g(h(f(x)))
k(x,h(x),a()) -> h(x)
k(f(x),y,x) -> f(x)
Weak DP Rules:
Weak TRS Rules:
Signature:
{f/1,h/1,k/3} / {a/0,g/1}
Obligation:
Innermost
basic terms: {f,h,k}/{a,g}
Applied Processor:
Bounds {initialAutomaton = minimal, enrichment = match}
Proof:
The problem is match-bounded by 2.
The enriched problem is compatible with follwoing automaton.
a_0() -> 2
a_1() -> 4
f_0(2) -> 1
f_1(2) -> 4
f_2(3) -> 6
g_0(2) -> 2
g_1(3) -> 1
g_1(3) -> 4
g_2(5) -> 3
h_0(2) -> 1
h_1(4) -> 3
h_2(6) -> 5
k_0(2,2,2) -> 1
*** 1.1 Progress [(O(1),O(1))] ***
Considered Problem:
Strict DP Rules:
Strict TRS Rules:
Weak DP Rules:
Weak TRS Rules:
f(a()) -> g(h(a()))
h(g(x)) -> g(h(f(x)))
k(x,h(x),a()) -> h(x)
k(f(x),y,x) -> f(x)
Signature:
{f/1,h/1,k/3} / {a/0,g/1}
Obligation:
Innermost
basic terms: {f,h,k}/{a,g}
Applied Processor:
EmptyProcessor
Proof:
The problem is already closed. The intended complexity is O(1).