*** 1 Progress [(O(1),O(n^1))] ***
Considered Problem:
Strict DP Rules:
Strict TRS Rules:
a__f(X) -> f(X)
a__f(X) -> g(h(f(X)))
mark(f(X)) -> a__f(mark(X))
mark(g(X)) -> g(X)
mark(h(X)) -> h(mark(X))
Weak DP Rules:
Weak TRS Rules:
Signature:
{a__f/1,mark/1} / {f/1,g/1,h/1}
Obligation:
Innermost
basic terms: {a__f,mark}/{f,g,h}
Applied Processor:
Bounds {initialAutomaton = minimal, enrichment = match}
Proof:
The problem is match-bounded by 2.
The enriched problem is compatible with follwoing automaton.
a__f_0(2) -> 1
a__f_1(4) -> 1
a__f_1(4) -> 4
f_0(2) -> 2
f_1(2) -> 1
f_2(4) -> 1
f_2(4) -> 4
g_0(2) -> 2
g_1(2) -> 1
g_1(2) -> 4
g_1(3) -> 1
g_2(5) -> 1
g_2(5) -> 4
h_0(2) -> 2
h_1(1) -> 3
h_1(4) -> 1
h_1(4) -> 4
h_2(1) -> 5
mark_0(2) -> 1
mark_1(2) -> 4
*** 1.1 Progress [(O(1),O(1))] ***
Considered Problem:
Strict DP Rules:
Strict TRS Rules:
Weak DP Rules:
Weak TRS Rules:
a__f(X) -> f(X)
a__f(X) -> g(h(f(X)))
mark(f(X)) -> a__f(mark(X))
mark(g(X)) -> g(X)
mark(h(X)) -> h(mark(X))
Signature:
{a__f/1,mark/1} / {f/1,g/1,h/1}
Obligation:
Innermost
basic terms: {a__f,mark}/{f,g,h}
Applied Processor:
EmptyProcessor
Proof:
The problem is already closed. The intended complexity is O(1).