*** 1 Progress [(O(1),O(n^1))] ***
Considered Problem:
Strict DP Rules:
Strict TRS Rules:
a(0(),x) -> c(c(x))
c(c(x)) -> b(c(b(c(x))))
c(c(b(c(x)))) -> b(a(0(),c(x)))
Weak DP Rules:
Weak TRS Rules:
Signature:
{a/2,c/1} / {0/0,b/1}
Obligation:
Innermost
basic terms: {a,c}/{0,b}
Applied Processor:
Bounds {initialAutomaton = perSymbol, enrichment = match}
Proof:
The problem is match-bounded by 2.
The enriched problem is compatible with follwoing automaton.
0_0() -> 1
a_0(1,1) -> 2
a_0(1,3) -> 2
a_0(3,1) -> 2
a_0(3,3) -> 2
b_0(1) -> 3
b_0(3) -> 3
b_2(6) -> 2
b_2(8) -> 7
c_0(1) -> 4
c_0(3) -> 4
c_1(1) -> 5
c_1(3) -> 5
c_1(5) -> 2
c_2(1) -> 8
c_2(3) -> 8
c_2(7) -> 6
*** 1.1 Progress [(O(1),O(1))] ***
Considered Problem:
Strict DP Rules:
Strict TRS Rules:
Weak DP Rules:
Weak TRS Rules:
a(0(),x) -> c(c(x))
c(c(x)) -> b(c(b(c(x))))
c(c(b(c(x)))) -> b(a(0(),c(x)))
Signature:
{a/2,c/1} / {0/0,b/1}
Obligation:
Innermost
basic terms: {a,c}/{0,b}
Applied Processor:
EmptyProcessor
Proof:
The problem is already closed. The intended complexity is O(1).