Tool CaT
Execution Time | Unknown |
---|
Answer | YES(?,O(n^1)) |
---|
Input | SK90 4.16 |
---|
stdout:
YES(?,O(n^1))
Problem:
f(0()) -> s(0())
f(s(0())) -> s(s(0()))
f(s(0())) -> *(s(s(0())),f(0()))
f(+(x,s(0()))) -> +(s(s(0())),f(x))
f(+(x,y)) -> *(f(x),f(y))
Proof:
Bounds Processor:
bound: 2
enrichment: match
automaton:
final states: {5}
transitions:
*1(5,9) -> 10,5
*1(10,10) -> 10,5
f1(7) -> 9*
f1(2) -> 10*
f1(4) -> 10*
f1(1) -> 10*
f1(3) -> 10*
+1(5,10) -> 10,5
s1(5) -> 10,5
s1(7) -> 10,5
01() -> 7*
s2(12) -> 9*
f0(2) -> 5*
f0(4) -> 5*
f0(1) -> 5*
f0(3) -> 5*
02() -> 12*
00() -> 1*
s0(2) -> 2*
s0(4) -> 2*
s0(1) -> 2*
s0(3) -> 2*
*0(3,1) -> 3*
*0(3,3) -> 3*
*0(4,2) -> 3*
*0(4,4) -> 3*
*0(1,2) -> 3*
*0(1,4) -> 3*
*0(2,1) -> 3*
*0(2,3) -> 3*
*0(3,2) -> 3*
*0(3,4) -> 3*
*0(4,1) -> 3*
*0(4,3) -> 3*
*0(1,1) -> 3*
*0(1,3) -> 3*
*0(2,2) -> 3*
*0(2,4) -> 3*
+0(3,1) -> 4*
+0(3,3) -> 4*
+0(4,2) -> 4*
+0(4,4) -> 4*
+0(1,2) -> 4*
+0(1,4) -> 4*
+0(2,1) -> 4*
+0(2,3) -> 4*
+0(3,2) -> 4*
+0(3,4) -> 4*
+0(4,1) -> 4*
+0(4,3) -> 4*
+0(1,1) -> 4*
+0(1,3) -> 4*
+0(2,2) -> 4*
+0(2,4) -> 4*
problem:
QedTool IRC1
Execution Time | Unknown |
---|
Answer | YES(?,O(n^1)) |
---|
Input | SK90 4.16 |
---|
stdout:
YES(?,O(n^1))
Tool IRC2
Execution Time | Unknown |
---|
Answer | YES(?,O(n^1)) |
---|
Input | SK90 4.16 |
---|
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(0()) -> s(0())
, f(s(0())) -> s(s(0()))
, f(s(0())) -> *(s(s(0())), f(0()))
, f(+(x, s(0()))) -> +(s(s(0())), f(x))
, f(+(x, y)) -> *(f(x), f(y))}
Proof Output:
'Bounds with minimal-enrichment and initial automaton 'match'' proved the best result:
Details:
--------
'Bounds with minimal-enrichment and initial automaton 'match'' succeeded with the following output:
'Bounds with minimal-enrichment and initial automaton 'match''
--------------------------------------------------------------
Answer: YES(?,O(n^1))
Input Problem: innermost runtime-complexity with respect to
Rules:
{ f(0()) -> s(0())
, f(s(0())) -> s(s(0()))
, f(s(0())) -> *(s(s(0())), f(0()))
, f(+(x, s(0()))) -> +(s(s(0())), f(x))
, f(+(x, y)) -> *(f(x), f(y))}
Proof Output:
The problem is match-bounded by 2.
The enriched problem is compatible with the following automaton:
{ f_0(2) -> 1
, f_1(2) -> 5
, f_1(3) -> 4
, 0_0() -> 2
, 0_1() -> 3
, 0_2() -> 6
, s_0(2) -> 2
, s_1(1) -> 1
, s_1(3) -> 1
, s_1(3) -> 5
, s_1(5) -> 5
, s_2(6) -> 4
, *_0(2, 2) -> 2
, *_1(1, 4) -> 1
, *_1(5, 4) -> 5
, *_1(5, 5) -> 1
, *_1(5, 5) -> 5
, +_0(2, 2) -> 2
, +_1(1, 5) -> 1
, +_1(5, 5) -> 5}Tool RC1
Execution Time | Unknown |
---|
Answer | YES(?,O(n^1)) |
---|
Input | SK90 4.16 |
---|
stdout:
YES(?,O(n^1))
Tool RC2
Execution Time | Unknown |
---|
Answer | YES(?,O(n^1)) |
---|
Input | SK90 4.16 |
---|
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(0()) -> s(0())
, f(s(0())) -> s(s(0()))
, f(s(0())) -> *(s(s(0())), f(0()))
, f(+(x, s(0()))) -> +(s(s(0())), f(x))
, f(+(x, y)) -> *(f(x), f(y))}
Proof Output:
'Bounds with minimal-enrichment and initial automaton 'match'' proved the best result:
Details:
--------
'Bounds with minimal-enrichment and initial automaton 'match'' succeeded with the following output:
'Bounds with minimal-enrichment and initial automaton 'match''
--------------------------------------------------------------
Answer: YES(?,O(n^1))
Input Problem: runtime-complexity with respect to
Rules:
{ f(0()) -> s(0())
, f(s(0())) -> s(s(0()))
, f(s(0())) -> *(s(s(0())), f(0()))
, f(+(x, s(0()))) -> +(s(s(0())), f(x))
, f(+(x, y)) -> *(f(x), f(y))}
Proof Output:
The problem is match-bounded by 2.
The enriched problem is compatible with the following automaton:
{ f_0(2) -> 1
, f_1(2) -> 5
, f_1(3) -> 4
, 0_0() -> 2
, 0_1() -> 3
, 0_2() -> 6
, s_0(2) -> 2
, s_1(1) -> 1
, s_1(3) -> 1
, s_1(3) -> 5
, s_1(5) -> 5
, s_2(6) -> 4
, *_0(2, 2) -> 2
, *_1(1, 4) -> 1
, *_1(5, 4) -> 5
, *_1(5, 5) -> 1
, *_1(5, 5) -> 5
, +_0(2, 2) -> 2
, +_1(1, 5) -> 1
, +_1(5, 5) -> 5}Tool pair1rc
Execution Time | Unknown |
---|
Answer | YES(?,O(n^1)) |
---|
Input | SK90 4.16 |
---|
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ f(0()) -> s(0())
, f(s(0())) -> s(s(0()))
, f(s(0())) -> *(s(s(0())), f(0()))
, f(+(x, s(0()))) -> +(s(s(0())), f(x))
, f(+(x, y)) -> *(f(x), f(y))}
StartTerms: basic terms
Strategy: none
Certificate: YES(?,O(n^1))
Application of 'pair1 (timeout of 60.0 seconds)':
-------------------------------------------------
The processor is not applicable, reason is:
Input problem is not restricted to innermost rewriting
We abort the transformation and continue with the subprocessor on the problem
Strict Trs:
{ f(0()) -> s(0())
, f(s(0())) -> s(s(0()))
, f(s(0())) -> *(s(s(0())), f(0()))
, f(+(x, s(0()))) -> +(s(s(0())), f(x))
, f(+(x, y)) -> *(f(x), f(y))}
StartTerms: basic terms
Strategy: none
1) 'Fastest' proved the goal fastest:
'Fastest' proved the goal fastest:
'Bounds with minimal-enrichment and initial automaton 'match'' proved the goal fastest:
The problem is match-bounded by 2.
The enriched problem is compatible with the following automaton:
{ f_0(2) -> 1
, f_1(2) -> 5
, f_1(3) -> 4
, 0_0() -> 2
, 0_1() -> 3
, 0_2() -> 6
, s_0(2) -> 2
, s_1(1) -> 1
, s_1(3) -> 1
, s_1(3) -> 5
, s_1(5) -> 5
, s_2(6) -> 4
, *_0(2, 2) -> 2
, *_1(1, 4) -> 1
, *_1(5, 4) -> 5
, *_1(5, 5) -> 1
, *_1(5, 5) -> 5
, +_0(2, 2) -> 2
, +_1(1, 5) -> 1
, +_1(5, 5) -> 5}
Hurray, we answered YES(?,O(n^1))Tool pair2rc
Execution Time | Unknown |
---|
Answer | YES(?,O(n^1)) |
---|
Input | SK90 4.16 |
---|
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ f(0()) -> s(0())
, f(s(0())) -> s(s(0()))
, f(s(0())) -> *(s(s(0())), f(0()))
, f(+(x, s(0()))) -> +(s(s(0())), f(x))
, f(+(x, y)) -> *(f(x), f(y))}
StartTerms: basic terms
Strategy: none
Certificate: YES(?,O(n^1))
Application of 'pair2 (timeout of 60.0 seconds)':
-------------------------------------------------
The processor is not applicable, reason is:
Input problem is not restricted to innermost rewriting
We abort the transformation and continue with the subprocessor on the problem
Strict Trs:
{ f(0()) -> s(0())
, f(s(0())) -> s(s(0()))
, f(s(0())) -> *(s(s(0())), f(0()))
, f(+(x, s(0()))) -> +(s(s(0())), f(x))
, f(+(x, y)) -> *(f(x), f(y))}
StartTerms: basic terms
Strategy: none
1) 'Fastest' proved the goal fastest:
'Fastest' proved the goal fastest:
'Bounds with minimal-enrichment and initial automaton 'match'' proved the goal fastest:
The problem is match-bounded by 2.
The enriched problem is compatible with the following automaton:
{ f_0(2) -> 1
, f_1(2) -> 5
, f_1(3) -> 4
, 0_0() -> 2
, 0_1() -> 3
, 0_2() -> 6
, s_0(2) -> 2
, s_1(1) -> 1
, s_1(3) -> 1
, s_1(3) -> 5
, s_1(5) -> 5
, s_2(6) -> 4
, *_0(2, 2) -> 2
, *_1(1, 4) -> 1
, *_1(5, 4) -> 5
, *_1(5, 5) -> 1
, *_1(5, 5) -> 5
, +_0(2, 2) -> 2
, +_1(1, 5) -> 1
, +_1(5, 5) -> 5}
Hurray, we answered YES(?,O(n^1))Tool pair3irc
Execution Time | Unknown |
---|
Answer | YES(?,O(n^1)) |
---|
Input | SK90 4.16 |
---|
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ f(0()) -> s(0())
, f(s(0())) -> s(s(0()))
, f(s(0())) -> *(s(s(0())), f(0()))
, f(+(x, s(0()))) -> +(s(s(0())), f(x))
, f(+(x, y)) -> *(f(x), f(y))}
StartTerms: basic terms
Strategy: innermost
Certificate: YES(?,O(n^1))
Application of 'pair3 (timeout of 60.0 seconds)':
-------------------------------------------------
The input problem contains no overlaps that give rise to inapplicable rules.
We abort the transformation and continue with the subprocessor on the problem
Strict Trs:
{ f(0()) -> s(0())
, f(s(0())) -> s(s(0()))
, f(s(0())) -> *(s(s(0())), f(0()))
, f(+(x, s(0()))) -> +(s(s(0())), f(x))
, f(+(x, y)) -> *(f(x), f(y))}
StartTerms: basic terms
Strategy: innermost
1) 'Fastest' proved the goal fastest:
'Fastest' proved the goal fastest:
'Bounds with minimal-enrichment and initial automaton 'match'' proved the goal fastest:
The problem is match-bounded by 2.
The enriched problem is compatible with the following automaton:
{ f_0(2) -> 1
, f_1(2) -> 5
, f_1(3) -> 4
, 0_0() -> 2
, 0_1() -> 3
, 0_2() -> 6
, s_0(2) -> 2
, s_1(1) -> 1
, s_1(3) -> 1
, s_1(3) -> 5
, s_1(5) -> 5
, s_2(6) -> 4
, *_0(2, 2) -> 2
, *_1(1, 4) -> 1
, *_1(5, 4) -> 5
, *_1(5, 5) -> 1
, *_1(5, 5) -> 5
, +_0(2, 2) -> 2
, +_1(1, 5) -> 1
, +_1(5, 5) -> 5}
Hurray, we answered YES(?,O(n^1))Tool pair3rc
Execution Time | Unknown |
---|
Answer | YES(?,O(n^1)) |
---|
Input | SK90 4.16 |
---|
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ f(0()) -> s(0())
, f(s(0())) -> s(s(0()))
, f(s(0())) -> *(s(s(0())), f(0()))
, f(+(x, s(0()))) -> +(s(s(0())), f(x))
, f(+(x, y)) -> *(f(x), f(y))}
StartTerms: basic terms
Strategy: none
Certificate: YES(?,O(n^1))
Application of 'pair3 (timeout of 60.0 seconds)':
-------------------------------------------------
The processor is not applicable, reason is:
Input problem is not restricted to innermost rewriting
We abort the transformation and continue with the subprocessor on the problem
Strict Trs:
{ f(0()) -> s(0())
, f(s(0())) -> s(s(0()))
, f(s(0())) -> *(s(s(0())), f(0()))
, f(+(x, s(0()))) -> +(s(s(0())), f(x))
, f(+(x, y)) -> *(f(x), f(y))}
StartTerms: basic terms
Strategy: none
1) 'Fastest' proved the goal fastest:
'Fastest' proved the goal fastest:
'Bounds with perSymbol-enrichment and initial automaton 'match'' proved the goal fastest:
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_0(4) -> 1
, f_0(5) -> 1
, f_1(2) -> 8
, f_1(3) -> 8
, f_1(4) -> 8
, f_1(5) -> 8
, f_1(6) -> 7
, 0_0() -> 2
, 0_1() -> 6
, 0_2() -> 9
, s_0(2) -> 3
, s_0(3) -> 3
, s_0(4) -> 3
, s_0(5) -> 3
, s_1(1) -> 1
, s_1(6) -> 1
, s_1(6) -> 8
, s_1(8) -> 8
, s_2(9) -> 7
, *_0(2, 2) -> 4
, *_0(2, 3) -> 4
, *_0(2, 4) -> 4
, *_0(2, 5) -> 4
, *_0(3, 2) -> 4
, *_0(3, 3) -> 4
, *_0(3, 4) -> 4
, *_0(3, 5) -> 4
, *_0(4, 2) -> 4
, *_0(4, 3) -> 4
, *_0(4, 4) -> 4
, *_0(4, 5) -> 4
, *_0(5, 2) -> 4
, *_0(5, 3) -> 4
, *_0(5, 4) -> 4
, *_0(5, 5) -> 4
, *_1(1, 7) -> 1
, *_1(8, 7) -> 8
, *_1(8, 8) -> 1
, *_1(8, 8) -> 8
, +_0(2, 2) -> 5
, +_0(2, 3) -> 5
, +_0(2, 4) -> 5
, +_0(2, 5) -> 5
, +_0(3, 2) -> 5
, +_0(3, 3) -> 5
, +_0(3, 4) -> 5
, +_0(3, 5) -> 5
, +_0(4, 2) -> 5
, +_0(4, 3) -> 5
, +_0(4, 4) -> 5
, +_0(4, 5) -> 5
, +_0(5, 2) -> 5
, +_0(5, 3) -> 5
, +_0(5, 4) -> 5
, +_0(5, 5) -> 5
, +_1(1, 8) -> 1
, +_1(8, 8) -> 8}
Hurray, we answered YES(?,O(n^1))Tool rc
Execution Time | Unknown |
---|
Answer | YES(?,O(n^1)) |
---|
Input | SK90 4.16 |
---|
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ f(0()) -> s(0())
, f(s(0())) -> s(s(0()))
, f(s(0())) -> *(s(s(0())), f(0()))
, f(+(x, s(0()))) -> +(s(s(0())), f(x))
, f(+(x, y)) -> *(f(x), f(y))}
StartTerms: basic terms
Strategy: none
Certificate: YES(?,O(n^1))
Application of 'rc (timeout of 60.0 seconds)':
----------------------------------------------
'Fastest' proved the goal fastest:
'Fastest' proved the goal fastest:
'Bounds with minimal-enrichment and initial automaton 'match' (timeout of 100.0 seconds)' proved the goal fastest:
The problem is match-bounded by 2.
The enriched problem is compatible with the following automaton:
{ f_0(2) -> 1
, f_1(2) -> 5
, f_1(3) -> 4
, 0_0() -> 2
, 0_1() -> 3
, 0_2() -> 6
, s_0(2) -> 2
, s_1(1) -> 1
, s_1(3) -> 1
, s_1(3) -> 5
, s_1(5) -> 5
, s_2(6) -> 4
, *_0(2, 2) -> 2
, *_1(1, 4) -> 1
, *_1(5, 4) -> 5
, *_1(5, 5) -> 1
, *_1(5, 5) -> 5
, +_0(2, 2) -> 2
, +_1(1, 5) -> 1
, +_1(5, 5) -> 5}
Hurray, we answered YES(?,O(n^1))Tool tup3irc
Execution Time | 7.107702ms |
---|
Answer | YES(?,O(n^1)) |
---|
Input | SK90 4.16 |
---|
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ f(0()) -> s(0())
, f(s(0())) -> s(s(0()))
, f(s(0())) -> *(s(s(0())), f(0()))
, f(+(x, s(0()))) -> +(s(s(0())), f(x))
, f(+(x, y)) -> *(f(x), f(y))}
StartTerms: basic terms
Strategy: innermost
Certificate: YES(?,O(n^1))
Application of 'tup3 (timeout of 60.0 seconds)':
------------------------------------------------
The input problem contains no overlaps that give rise to inapplicable rules.
We abort the transformation and continue with the subprocessor on the problem
Strict Trs:
{ f(0()) -> s(0())
, f(s(0())) -> s(s(0()))
, f(s(0())) -> *(s(s(0())), f(0()))
, f(+(x, s(0()))) -> +(s(s(0())), f(x))
, f(+(x, y)) -> *(f(x), f(y))}
StartTerms: basic terms
Strategy: innermost
1) 'Fastest' proved the goal fastest:
'Fastest' proved the goal fastest:
'Bounds with minimal-enrichment and initial automaton 'match'' proved the goal fastest:
The problem is match-bounded by 2.
The enriched problem is compatible with the following automaton:
{ f_0(2) -> 1
, f_1(2) -> 5
, f_1(3) -> 4
, 0_0() -> 2
, 0_1() -> 3
, 0_2() -> 6
, s_0(2) -> 2
, s_1(1) -> 1
, s_1(3) -> 1
, s_1(3) -> 5
, s_1(5) -> 5
, s_2(6) -> 4
, *_0(2, 2) -> 2
, *_1(1, 4) -> 1
, *_1(5, 4) -> 5
, *_1(5, 5) -> 1
, *_1(5, 5) -> 5
, +_0(2, 2) -> 2
, +_1(1, 5) -> 1
, +_1(5, 5) -> 5}
Hurray, we answered YES(?,O(n^1))