Tool CaT
stdout:
YES(?,O(n^1))
Problem:
f(c(X,s(Y))) -> f(c(s(X),Y))
g(c(s(X),Y)) -> f(c(X,s(Y)))
Proof:
Bounds Processor:
bound: 2
enrichment: match
automaton:
final states: {4,3}
transitions:
f1(9) -> 4*
f1(8) -> 3*
c1(16,2) -> 9*
c1(7,1) -> 8*
c1(2,7) -> 9*
c1(16,1) -> 9*
c1(1,7) -> 9*
c1(7,2) -> 8*
s1(7) -> 7*
s1(2) -> 7*
s1(16) -> 16*
s1(1) -> 7*
s1(13) -> 16*
f2(14) -> 4*
c2(13,1) -> 14*
c2(13,7) -> 14*
c2(13,2) -> 14*
f0(2) -> 3*
f0(1) -> 3*
s2(2) -> 13*
s2(1) -> 13*
s2(13) -> 13*
c0(1,2) -> 1*
c0(2,1) -> 1*
c0(1,1) -> 1*
c0(2,2) -> 1*
s0(2) -> 2*
s0(1) -> 2*
g0(2) -> 4*
g0(1) -> 4*
problem:
QedTool IRC1
stdout:
YES(?,O(n^1))
Tool IRC2
stdout:
YES(?,O(n^1))
'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer: YES(?,O(n^1))
Input Problem: innermost runtime-complexity with respect to
Rules:
{ f(c(X, s(Y))) -> f(c(s(X), Y))
, g(c(s(X), Y)) -> f(c(X, s(Y)))}
Proof Output:
'Bounds with perSymbol-enrichment and initial automaton 'match'' proved the best result:
Details:
--------
'Bounds with perSymbol-enrichment and initial automaton 'match'' succeeded with the following output:
'Bounds with perSymbol-enrichment and initial automaton 'match''
----------------------------------------------------------------
Answer: YES(?,O(n^1))
Input Problem: innermost runtime-complexity with respect to
Rules:
{ f(c(X, s(Y))) -> f(c(s(X), Y))
, g(c(s(X), Y)) -> f(c(X, s(Y)))}
Proof Output:
The problem is match-bounded by 2.
The enriched problem is compatible with the following automaton:
{ f_0(2) -> 1
, f_0(3) -> 1
, f_1(5) -> 1
, f_1(7) -> 4
, f_2(8) -> 4
, c_0(2, 2) -> 2
, c_0(2, 3) -> 2
, c_0(3, 2) -> 2
, c_0(3, 3) -> 2
, c_1(2, 6) -> 7
, c_1(3, 6) -> 7
, c_1(6, 2) -> 5
, c_1(6, 3) -> 5
, c_1(10, 2) -> 7
, c_1(10, 3) -> 7
, c_2(9, 2) -> 8
, c_2(9, 3) -> 8
, c_2(9, 6) -> 8
, s_0(2) -> 3
, s_0(3) -> 3
, s_1(2) -> 6
, s_1(3) -> 6
, s_1(6) -> 6
, s_1(9) -> 10
, s_1(10) -> 10
, s_2(2) -> 9
, s_2(3) -> 9
, s_2(9) -> 9
, g_0(2) -> 4
, g_0(3) -> 4}Tool RC1
stdout:
YES(?,O(n^1))
Tool RC2
stdout:
YES(?,O(n^1))
'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer: YES(?,O(n^1))
Input Problem: runtime-complexity with respect to
Rules:
{ f(c(X, s(Y))) -> f(c(s(X), Y))
, g(c(s(X), Y)) -> f(c(X, s(Y)))}
Proof Output:
'Bounds with perSymbol-enrichment and initial automaton 'match'' proved the best result:
Details:
--------
'Bounds with perSymbol-enrichment and initial automaton 'match'' succeeded with the following output:
'Bounds with perSymbol-enrichment and initial automaton 'match''
----------------------------------------------------------------
Answer: YES(?,O(n^1))
Input Problem: runtime-complexity with respect to
Rules:
{ f(c(X, s(Y))) -> f(c(s(X), Y))
, g(c(s(X), Y)) -> f(c(X, s(Y)))}
Proof Output:
The problem is match-bounded by 2.
The enriched problem is compatible with the following automaton:
{ f_0(2) -> 1
, f_0(3) -> 1
, f_1(5) -> 1
, f_1(7) -> 4
, f_2(8) -> 4
, c_0(2, 2) -> 2
, c_0(2, 3) -> 2
, c_0(3, 2) -> 2
, c_0(3, 3) -> 2
, c_1(2, 6) -> 7
, c_1(3, 6) -> 7
, c_1(6, 2) -> 5
, c_1(6, 3) -> 5
, c_1(10, 2) -> 7
, c_1(10, 3) -> 7
, c_2(9, 2) -> 8
, c_2(9, 3) -> 8
, c_2(9, 6) -> 8
, s_0(2) -> 3
, s_0(3) -> 3
, s_1(2) -> 6
, s_1(3) -> 6
, s_1(6) -> 6
, s_1(9) -> 10
, s_1(10) -> 10
, s_2(2) -> 9
, s_2(3) -> 9
, s_2(9) -> 9
, g_0(2) -> 4
, g_0(3) -> 4}