*** 1 Progress [(O(1),O(n^1))] ***
Considered Problem:
Strict DP Rules:
Strict TRS Rules:
rev(++(x,x)) -> rev(x)
rev(++(x,y)) -> ++(rev(y),rev(x))
rev(a()) -> a()
rev(b()) -> b()
Weak DP Rules:
Weak TRS Rules:
Signature:
{rev/1} / {++/2,a/0,b/0}
Obligation:
Full
basic terms: {rev}/{++,a,b}
Applied Processor:
ToInnermost
Proof:
switch to innermost, as the system is overlay and right linear and does not contain weak rules
*** 1.1 Progress [(O(1),O(n^1))] ***
Considered Problem:
Strict DP Rules:
Strict TRS Rules:
rev(++(x,x)) -> rev(x)
rev(++(x,y)) -> ++(rev(y),rev(x))
rev(a()) -> a()
rev(b()) -> b()
Weak DP Rules:
Weak TRS Rules:
Signature:
{rev/1} / {++/2,a/0,b/0}
Obligation:
Innermost
basic terms: {rev}/{++,a,b}
Applied Processor:
Bounds {initialAutomaton = minimal, enrichment = match}
Proof:
The problem is match-bounded by 1.
The enriched problem is compatible with follwoing automaton.
++_0(2,2) -> 2
++_1(1,1) -> 1
a_0() -> 2
a_1() -> 1
b_0() -> 2
b_1() -> 1
rev_0(2) -> 1
rev_1(2) -> 1
*** 1.1.1 Progress [(O(1),O(1))] ***
Considered Problem:
Strict DP Rules:
Strict TRS Rules:
Weak DP Rules:
Weak TRS Rules:
rev(++(x,x)) -> rev(x)
rev(++(x,y)) -> ++(rev(y),rev(x))
rev(a()) -> a()
rev(b()) -> b()
Signature:
{rev/1} / {++/2,a/0,b/0}
Obligation:
Innermost
basic terms: {rev}/{++,a,b}
Applied Processor:
EmptyProcessor
Proof:
The problem is already closed. The intended complexity is O(1).