Tool CaT
Execution Time | Unknown |
---|
Answer | MAYBE |
---|
Input | SK90 2.40 |
---|
stdout:
MAYBE
Problem:
or(true(),y) -> true()
or(x,true()) -> true()
or(false(),false()) -> false()
mem(x,nil()) -> false()
mem(x,set(y)) -> =(x,y)
mem(x,union(y,z)) -> or(mem(x,y),mem(x,z))
Proof:
OpenTool IRC1
Execution Time | Unknown |
---|
Answer | MAYBE |
---|
Input | SK90 2.40 |
---|
stdout:
MAYBE
Tool IRC2
Execution Time | Unknown |
---|
Answer | YES(?,O(n^1)) |
---|
Input | SK90 2.40 |
---|
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:
{ or(true(), y) -> true()
, or(x, true()) -> true()
, or(false(), false()) -> false()
, mem(x, nil()) -> false()
, mem(x, set(y)) -> =(x, y)
, mem(x, union(y, z)) -> or(mem(x, y), mem(x, z))}
Proof Output:
'matrix-interpretation of dimension 1' proved the best result:
Details:
--------
'matrix-interpretation of dimension 1' succeeded with the following output:
'matrix-interpretation of dimension 1'
--------------------------------------
Answer: YES(?,O(n^1))
Input Problem: innermost runtime-complexity with respect to
Rules:
{ or(true(), y) -> true()
, or(x, true()) -> true()
, or(false(), false()) -> false()
, mem(x, nil()) -> false()
, mem(x, set(y)) -> =(x, y)
, mem(x, union(y, z)) -> or(mem(x, y), mem(x, z))}
Proof Output:
The following argument positions are usable:
Uargs(or) = {1, 2}, Uargs(mem) = {}, Uargs(set) = {},
Uargs(=) = {}, Uargs(union) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
or(x1, x2) = [1] x1 + [1] x2 + [1]
true() = [1]
false() = [4]
mem(x1, x2) = [0] x1 + [2] x2 + [0]
nil() = [4]
set(x1) = [1] x1 + [1]
=(x1, x2) = [0] x1 + [0] x2 + [1]
union(x1, x2) = [1] x1 + [1] x2 + [2]Tool RC1
Execution Time | Unknown |
---|
Answer | MAYBE |
---|
Input | SK90 2.40 |
---|
stdout:
MAYBE
Tool RC2
Execution Time | Unknown |
---|
Answer | YES(?,O(n^1)) |
---|
Input | SK90 2.40 |
---|
stdout:
YES(?,O(n^1))
'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer: YES(?,O(n^1))
Input Problem: runtime-complexity with respect to
Rules:
{ or(true(), y) -> true()
, or(x, true()) -> true()
, or(false(), false()) -> false()
, mem(x, nil()) -> false()
, mem(x, set(y)) -> =(x, y)
, mem(x, union(y, z)) -> or(mem(x, y), mem(x, z))}
Proof Output:
'matrix-interpretation of dimension 1' proved the best result:
Details:
--------
'matrix-interpretation of dimension 1' succeeded with the following output:
'matrix-interpretation of dimension 1'
--------------------------------------
Answer: YES(?,O(n^1))
Input Problem: runtime-complexity with respect to
Rules:
{ or(true(), y) -> true()
, or(x, true()) -> true()
, or(false(), false()) -> false()
, mem(x, nil()) -> false()
, mem(x, set(y)) -> =(x, y)
, mem(x, union(y, z)) -> or(mem(x, y), mem(x, z))}
Proof Output:
The following argument positions are usable:
Uargs(or) = {1, 2}, Uargs(mem) = {}, Uargs(set) = {},
Uargs(=) = {}, Uargs(union) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
or(x1, x2) = [1] x1 + [1] x2 + [1]
true() = [1]
false() = [4]
mem(x1, x2) = [0] x1 + [2] x2 + [0]
nil() = [4]
set(x1) = [1] x1 + [1]
=(x1, x2) = [0] x1 + [0] x2 + [1]
union(x1, x2) = [1] x1 + [1] x2 + [2]Tool pair1rc
Execution Time | Unknown |
---|
Answer | YES(?,O(n^1)) |
---|
Input | SK90 2.40 |
---|
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ or(true(), y) -> true()
, or(x, true()) -> true()
, or(false(), false()) -> false()
, mem(x, nil()) -> false()
, mem(x, set(y)) -> =(x, y)
, mem(x, union(y, z)) -> or(mem(x, y), mem(x, z))}
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:
{ or(true(), y) -> true()
, or(x, true()) -> true()
, or(false(), false()) -> false()
, mem(x, nil()) -> false()
, mem(x, set(y)) -> =(x, y)
, mem(x, union(y, z)) -> or(mem(x, y), mem(x, z))}
StartTerms: basic terms
Strategy: none
1) 'Fastest' proved the goal fastest:
'Sequentially' proved the goal fastest:
'Fastest' succeeded:
'matrix-interpretation of dimension 2 (timeout of 100.0 seconds)' proved the goal fastest:
The following argument positions are usable:
Uargs(or) = {1, 2}, Uargs(mem) = {}, Uargs(set) = {},
Uargs(=) = {}, Uargs(union) = {}
We have the following constructor-restricted (at most 1 in the main diagonals) matrix interpretation:
Interpretation Functions:
or(x1, x2) = [1 2] x1 + [1 2] x2 + [1]
[0 2] [0 1] [0]
true() = [0]
[2]
false() = [0]
[0]
mem(x1, x2) = [0 0] x1 + [1 1] x2 + [1]
[0 0] [0 0] [0]
nil() = [0]
[0]
set(x1) = [1 2] x1 + [0]
[0 0] [0]
=(x1, x2) = [0 0] x1 + [1 0] x2 + [0]
[0 0] [0 0] [0]
union(x1, x2) = [1 1] x1 + [1 1] x2 + [2]
[0 0] [0 0] [1]
Hurray, we answered YES(?,O(n^1))Tool pair2rc
Execution Time | Unknown |
---|
Answer | YES(?,O(n^1)) |
---|
Input | SK90 2.40 |
---|
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ or(true(), y) -> true()
, or(x, true()) -> true()
, or(false(), false()) -> false()
, mem(x, nil()) -> false()
, mem(x, set(y)) -> =(x, y)
, mem(x, union(y, z)) -> or(mem(x, y), mem(x, z))}
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:
{ or(true(), y) -> true()
, or(x, true()) -> true()
, or(false(), false()) -> false()
, mem(x, nil()) -> false()
, mem(x, set(y)) -> =(x, y)
, mem(x, union(y, z)) -> or(mem(x, y), mem(x, z))}
StartTerms: basic terms
Strategy: none
1) 'Fastest' proved the goal fastest:
'Sequentially' proved the goal fastest:
'Fastest' succeeded:
'matrix-interpretation of dimension 2 (timeout of 100.0 seconds)' proved the goal fastest:
The following argument positions are usable:
Uargs(or) = {1, 2}, Uargs(mem) = {}, Uargs(set) = {},
Uargs(=) = {}, Uargs(union) = {}
We have the following constructor-restricted (at most 1 in the main diagonals) matrix interpretation:
Interpretation Functions:
or(x1, x2) = [1 2] x1 + [1 2] x2 + [1]
[0 2] [0 1] [0]
true() = [0]
[2]
false() = [0]
[0]
mem(x1, x2) = [0 0] x1 + [1 1] x2 + [1]
[0 0] [0 0] [0]
nil() = [0]
[0]
set(x1) = [1 2] x1 + [0]
[0 0] [0]
=(x1, x2) = [0 0] x1 + [1 0] x2 + [0]
[0 0] [0 0] [0]
union(x1, x2) = [1 1] x1 + [1 1] x2 + [2]
[0 0] [0 0] [1]
Hurray, we answered YES(?,O(n^1))Tool pair3irc
Execution Time | Unknown |
---|
Answer | YES(?,O(n^1)) |
---|
Input | SK90 2.40 |
---|
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ or(true(), y) -> true()
, or(x, true()) -> true()
, or(false(), false()) -> false()
, mem(x, nil()) -> false()
, mem(x, set(y)) -> =(x, y)
, mem(x, union(y, z)) -> or(mem(x, y), mem(x, z))}
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:
{ or(true(), y) -> true()
, or(x, true()) -> true()
, or(false(), false()) -> false()
, mem(x, nil()) -> false()
, mem(x, set(y)) -> =(x, y)
, mem(x, union(y, z)) -> or(mem(x, y), mem(x, z))}
StartTerms: basic terms
Strategy: innermost
1) 'Fastest' proved the goal fastest:
'Sequentially' proved the goal fastest:
'Fastest' succeeded:
'matrix-interpretation of dimension 2 (timeout of 100.0 seconds)' proved the goal fastest:
The following argument positions are usable:
Uargs(or) = {1, 2}, Uargs(mem) = {}, Uargs(set) = {},
Uargs(=) = {}, Uargs(union) = {}
We have the following constructor-restricted (at most 1 in the main diagonals) matrix interpretation:
Interpretation Functions:
or(x1, x2) = [1 2] x1 + [1 2] x2 + [1]
[0 2] [0 1] [0]
true() = [0]
[2]
false() = [0]
[0]
mem(x1, x2) = [0 0] x1 + [1 1] x2 + [1]
[0 0] [0 0] [0]
nil() = [0]
[0]
set(x1) = [1 2] x1 + [0]
[0 0] [0]
=(x1, x2) = [0 0] x1 + [1 0] x2 + [0]
[0 0] [0 0] [0]
union(x1, x2) = [1 1] x1 + [1 1] x2 + [2]
[0 0] [0 0] [1]
Hurray, we answered YES(?,O(n^1))Tool pair3rc
Execution Time | Unknown |
---|
Answer | YES(?,O(n^1)) |
---|
Input | SK90 2.40 |
---|
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ or(true(), y) -> true()
, or(x, true()) -> true()
, or(false(), false()) -> false()
, mem(x, nil()) -> false()
, mem(x, set(y)) -> =(x, y)
, mem(x, union(y, z)) -> or(mem(x, y), mem(x, z))}
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:
{ or(true(), y) -> true()
, or(x, true()) -> true()
, or(false(), false()) -> false()
, mem(x, nil()) -> false()
, mem(x, set(y)) -> =(x, y)
, mem(x, union(y, z)) -> or(mem(x, y), mem(x, z))}
StartTerms: basic terms
Strategy: none
1) 'Fastest' proved the goal fastest:
'Sequentially' proved the goal fastest:
'Fastest' succeeded:
'matrix-interpretation of dimension 2 (timeout of 100.0 seconds)' proved the goal fastest:
The following argument positions are usable:
Uargs(or) = {1, 2}, Uargs(mem) = {}, Uargs(set) = {},
Uargs(=) = {}, Uargs(union) = {}
We have the following constructor-restricted (at most 1 in the main diagonals) matrix interpretation:
Interpretation Functions:
or(x1, x2) = [1 2] x1 + [1 2] x2 + [1]
[0 2] [0 1] [0]
true() = [0]
[2]
false() = [0]
[0]
mem(x1, x2) = [0 0] x1 + [1 1] x2 + [1]
[0 0] [0 0] [0]
nil() = [0]
[0]
set(x1) = [1 2] x1 + [0]
[0 0] [0]
=(x1, x2) = [0 0] x1 + [1 0] x2 + [0]
[0 0] [0 0] [0]
union(x1, x2) = [1 1] x1 + [1 1] x2 + [2]
[0 0] [0 0] [1]
Hurray, we answered YES(?,O(n^1))Tool rc
Execution Time | Unknown |
---|
Answer | YES(?,O(n^1)) |
---|
Input | SK90 2.40 |
---|
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ or(true(), y) -> true()
, or(x, true()) -> true()
, or(false(), false()) -> false()
, mem(x, nil()) -> false()
, mem(x, set(y)) -> =(x, y)
, mem(x, union(y, z)) -> or(mem(x, y), mem(x, z))}
StartTerms: basic terms
Strategy: none
Certificate: YES(?,O(n^1))
Application of 'rc (timeout of 60.0 seconds)':
----------------------------------------------
'Fastest' proved the goal fastest:
'Sequentially' proved the goal fastest:
'Fastest' succeeded:
'matrix-interpretation of dimension 2 (timeout of 100.0 seconds)' proved the goal fastest:
The following argument positions are usable:
Uargs(or) = {1, 2}, Uargs(mem) = {}, Uargs(set) = {},
Uargs(=) = {}, Uargs(union) = {}
We have the following constructor-restricted (at most 1 in the main diagonals) matrix interpretation:
Interpretation Functions:
or(x1, x2) = [1 2] x1 + [1 2] x2 + [1]
[0 2] [0 1] [0]
true() = [0]
[2]
false() = [0]
[0]
mem(x1, x2) = [0 0] x1 + [1 1] x2 + [1]
[0 0] [0 0] [0]
nil() = [0]
[0]
set(x1) = [1 2] x1 + [0]
[0 0] [0]
=(x1, x2) = [0 0] x1 + [1 0] x2 + [0]
[0 0] [0 0] [0]
union(x1, x2) = [1 1] x1 + [1 1] x2 + [2]
[0 0] [0 0] [1]
Hurray, we answered YES(?,O(n^1))Tool tup3irc
Execution Time | 0.65342903ms |
---|
Answer | YES(?,O(n^1)) |
---|
Input | SK90 2.40 |
---|
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ or(true(), y) -> true()
, or(x, true()) -> true()
, or(false(), false()) -> false()
, mem(x, nil()) -> false()
, mem(x, set(y)) -> =(x, y)
, mem(x, union(y, z)) -> or(mem(x, y), mem(x, z))}
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:
{ or(true(), y) -> true()
, or(x, true()) -> true()
, or(false(), false()) -> false()
, mem(x, nil()) -> false()
, mem(x, set(y)) -> =(x, y)
, mem(x, union(y, z)) -> or(mem(x, y), mem(x, z))}
StartTerms: basic terms
Strategy: innermost
1) 'Fastest' proved the goal fastest:
'Sequentially' proved the goal fastest:
'Fastest' succeeded:
'matrix-interpretation of dimension 2 (timeout of 100.0 seconds)' proved the goal fastest:
The following argument positions are usable:
Uargs(or) = {1, 2}, Uargs(mem) = {}, Uargs(set) = {},
Uargs(=) = {}, Uargs(union) = {}
We have the following constructor-restricted (at most 1 in the main diagonals) matrix interpretation:
Interpretation Functions:
or(x1, x2) = [1 2] x1 + [1 2] x2 + [1]
[0 2] [0 1] [0]
true() = [0]
[2]
false() = [0]
[0]
mem(x1, x2) = [0 0] x1 + [1 1] x2 + [1]
[0 0] [0 0] [0]
nil() = [0]
[0]
set(x1) = [1 2] x1 + [0]
[0 0] [0]
=(x1, x2) = [0 0] x1 + [1 0] x2 + [0]
[0 0] [0 0] [0]
union(x1, x2) = [1 1] x1 + [1 1] x2 + [2]
[0 0] [0 0] [1]
Hurray, we answered YES(?,O(n^1))