Tool LMPO
stdout:
MAYBE
We consider the following Problem:
Strict Trs:
{ f(s(x), y) -> f(x, g(x, y))
, f(0(), y) -> y
, g(x, y) -> y}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
Tool MPO
stdout:
MAYBE
We consider the following Problem:
Strict Trs:
{ f(s(x), y) -> f(x, g(x, y))
, f(0(), y) -> y
, g(x, y) -> y}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
Tool POP*
stdout:
MAYBE
We consider the following Problem:
Strict Trs:
{ f(s(x), y) -> f(x, g(x, y))
, f(0(), y) -> y
, g(x, y) -> y}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
Tool POP* (PS)
Execution Time | 0.040 |
---|
Answer | YES(?,POLY) |
---|
Input | TCT 09 ma1 |
---|
stdout:
YES(?,POLY)
We consider the following Problem:
Strict Trs:
{ f(s(x), y) -> f(x, g(x, y))
, f(0(), y) -> y
, g(x, y) -> y}
StartTerms: basic terms
Strategy: innermost
Certificate: YES(?,POLY)
Proof:
The input was oriented with the instance of
Polynomial Path Order (PS) as induced by the safe mapping
safe(f) = {2}, safe(s) = {1}, safe(g) = {1, 2}, safe(0) = {}
and precedence
f > g .
Following symbols are considered recursive:
{f, g}
The recursion depth is 2 .
For your convenience, here are the oriented rules in predicative
notation (possibly applying argument filtering):
Strict DPs: {}
Weak DPs : {}
Strict Trs:
{ f(s(; x); y) -> f(x; g(; x, y))
, f(0(); y) -> y
, g(; x, y) -> y}
Weak Trs : {}
Hurray, we answered YES(?,POLY)
Tool Small POP*
stdout:
MAYBE
We consider the following Problem:
Strict Trs:
{ f(s(x), y) -> f(x, g(x, y))
, f(0(), y) -> y
, g(x, y) -> y}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
Tool Small POP* (PS)
Execution Time | 0.066 |
---|
Answer | YES(?,O(n^1)) |
---|
Input | TCT 09 ma1 |
---|
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ f(s(x), y) -> f(x, g(x, y))
, f(0(), y) -> y
, g(x, y) -> y}
StartTerms: basic terms
Strategy: innermost
Certificate: YES(?,O(n^1))
Proof:
The input was oriented with the instance of
Small Polynomial Path Order (WSC,
PS,
Nat 1-bounded) as induced by the safe mapping
safe(f) = {2}, safe(s) = {1}, safe(g) = {2}, safe(0) = {}
and precedence
f > g .
Following symbols are considered recursive:
{f}
The recursion depth is 1 .
For your convenience, here are the oriented rules in predicative
notation (possibly applying argument filtering):
Strict DPs: {}
Weak DPs : {}
Strict Trs:
{ f(s(; x); y) -> f(x; g(x; y))
, f(0(); y) -> y
, g(x; y) -> y}
Weak Trs : {}
Hurray, we answered YES(?,O(n^1))