interpretations
YES(?,O(n^1))
We are left with following problem, upon which TcT provides the
certificate YES(?,O(n^1)).
Strict Trs:
{ 0(1(2(3(4(x1))))) -> 0(2(3(1(4(x1)))))
, 0(5(1(2(3(4(x1)))))) -> 0(1(2(5(3(4(x1))))))
, 0(5(1(2(3(4(x1)))))) -> 0(5(2(1(3(4(x1))))))
, 0(5(1(2(3(4(x1)))))) -> 5(0(2(3(1(4(x1))))))
, 0(5(2(3(1(4(x1)))))) -> 0(1(5(2(3(4(x1)))))) }
Obligation:
innermost runtime complexity
Answer:
YES(?,O(n^1))
The following argument positions are usable:
Uargs(0) = {}, Uargs(1) = {}, Uargs(2) = {}, Uargs(3) = {},
Uargs(4) = {}, Uargs(5) = {}
TcT has computed following constructor-based matrix interpretation
satisfying not(EDA).
[0](x1) = [2] x1 + [0]
[1](x1) = [2]
[2](x1) = [0]
[3](x1) = [1] x1 + [1]
[4](x1) = [1]
[5](x1) = [1] x1 + [3]
This order satisfies following ordering constraints
[0(1(2(3(4(x1)))))] = [4]
> [0]
= [0(2(3(1(4(x1)))))]
[0(5(1(2(3(4(x1))))))] = [10]
> [4]
= [0(1(2(5(3(4(x1))))))]
[0(5(1(2(3(4(x1))))))] = [10]
> [6]
= [0(5(2(1(3(4(x1))))))]
[0(5(1(2(3(4(x1))))))] = [10]
> [3]
= [5(0(2(3(1(4(x1))))))]
[0(5(2(3(1(4(x1))))))] = [6]
> [4]
= [0(1(5(2(3(4(x1))))))]
Hurray, we answered YES(?,O(n^1))
lmpo
MAYBE
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict Trs:
{ 0(1(2(3(4(x1))))) -> 0(2(3(1(4(x1)))))
, 0(5(1(2(3(4(x1)))))) -> 0(1(2(5(3(4(x1))))))
, 0(5(1(2(3(4(x1)))))) -> 0(5(2(1(3(4(x1))))))
, 0(5(1(2(3(4(x1)))))) -> 5(0(2(3(1(4(x1))))))
, 0(5(2(3(1(4(x1)))))) -> 0(1(5(2(3(4(x1)))))) }
Obligation:
innermost runtime complexity
Answer:
MAYBE
The input cannot be shown compatible
Arrrr..
mpo
YES(?,PRIMREC)
We are left with following problem, upon which TcT provides the
certificate YES(?,PRIMREC).
Strict Trs:
{ 0(1(2(3(4(x1))))) -> 0(2(3(1(4(x1)))))
, 0(5(1(2(3(4(x1)))))) -> 0(1(2(5(3(4(x1))))))
, 0(5(1(2(3(4(x1)))))) -> 0(5(2(1(3(4(x1))))))
, 0(5(1(2(3(4(x1)))))) -> 5(0(2(3(1(4(x1))))))
, 0(5(2(3(1(4(x1)))))) -> 0(1(5(2(3(4(x1)))))) }
Obligation:
innermost runtime complexity
Answer:
YES(?,PRIMREC)
The input was oriented with the instance of'multiset path orders'
as induced by the precedence
1 > 2, 1 > 3, 5 > 1, 5 > 2, 0 ~ 5 .
Hurray, we answered YES(?,PRIMREC)
popstar
MAYBE
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict Trs:
{ 0(1(2(3(4(x1))))) -> 0(2(3(1(4(x1)))))
, 0(5(1(2(3(4(x1)))))) -> 0(1(2(5(3(4(x1))))))
, 0(5(1(2(3(4(x1)))))) -> 0(5(2(1(3(4(x1))))))
, 0(5(1(2(3(4(x1)))))) -> 5(0(2(3(1(4(x1))))))
, 0(5(2(3(1(4(x1)))))) -> 0(1(5(2(3(4(x1)))))) }
Obligation:
innermost runtime complexity
Answer:
MAYBE
The input cannot be shown compatible
Arrrr..
popstar-ps
MAYBE
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict Trs:
{ 0(1(2(3(4(x1))))) -> 0(2(3(1(4(x1)))))
, 0(5(1(2(3(4(x1)))))) -> 0(1(2(5(3(4(x1))))))
, 0(5(1(2(3(4(x1)))))) -> 0(5(2(1(3(4(x1))))))
, 0(5(1(2(3(4(x1)))))) -> 5(0(2(3(1(4(x1))))))
, 0(5(2(3(1(4(x1)))))) -> 0(1(5(2(3(4(x1)))))) }
Obligation:
innermost runtime complexity
Answer:
MAYBE
The input cannot be shown compatible
Arrrr..