*** 1 Progress [(O(1),O(n^1))] ***
Considered Problem:
Strict DP Rules:
Strict TRS Rules:
h(x,c(y,z)) -> h(c(s(y),x),z)
h(c(s(x),c(s(0()),y)),z) -> h(y,c(s(0()),c(x,z)))
Weak DP Rules:
Weak TRS Rules:
Signature:
{h/2} / {0/0,c/2,s/1}
Obligation:
Full
basic terms: {h}/{0,c,s}
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:
h(x,c(y,z)) -> h(c(s(y),x),z)
h(c(s(x),c(s(0()),y)),z) -> h(y,c(s(0()),c(x,z)))
Weak DP Rules:
Weak TRS Rules:
Signature:
{h/2} / {0/0,c/2,s/1}
Obligation:
Innermost
basic terms: {h}/{0,c,s}
Applied Processor:
Bounds {initialAutomaton = minimal, enrichment = match}
Proof:
The problem is match-bounded by 2.
The enriched problem is compatible with follwoing automaton.
0_0() -> 2
0_1() -> 8
c_0(2,2) -> 2
c_1(2,2) -> 7
c_1(2,5) -> 7
c_1(4,2) -> 3
c_1(4,3) -> 3
c_1(4,11) -> 3
c_1(6,5) -> 5
c_1(6,7) -> 5
c_2(10,2) -> 9
c_2(10,3) -> 9
c_2(10,9) -> 9
c_2(10,11) -> 9
c_2(12,9) -> 11
h_0(2,2) -> 1
h_1(2,5) -> 1
h_1(3,2) -> 1
h_1(3,5) -> 1
h_1(9,5) -> 1
h_1(11,5) -> 1
h_2(9,5) -> 1
h_2(9,7) -> 1
h_2(11,2) -> 1
h_2(11,5) -> 1
s_0(2) -> 2
s_1(2) -> 4
s_1(8) -> 6
s_2(2) -> 12
s_2(6) -> 10
*** 1.1.1 Progress [(O(1),O(1))] ***
Considered Problem:
Strict DP Rules:
Strict TRS Rules:
Weak DP Rules:
Weak TRS Rules:
h(x,c(y,z)) -> h(c(s(y),x),z)
h(c(s(x),c(s(0()),y)),z) -> h(y,c(s(0()),c(x,z)))
Signature:
{h/2} / {0/0,c/2,s/1}
Obligation:
Innermost
basic terms: {h}/{0,c,s}
Applied Processor:
EmptyProcessor
Proof:
The problem is already closed. The intended complexity is O(1).