Termination w.r.t. Q of the following Term Rewriting System could not be shown:
Q restricted rewrite system:
The TRS R consists of the following rules:
f(f(f(f(j, a), b), c), d) → f(f(a, b), f(f(a, d), c))
Q is empty.
↳ QTRS
↳ Overlay + Local Confluence
Q restricted rewrite system:
The TRS R consists of the following rules:
f(f(f(f(j, a), b), c), d) → f(f(a, b), f(f(a, d), c))
Q is empty.
The TRS is overlay and locally confluent. By [15] we can switch to innermost.
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
Q restricted rewrite system:
The TRS R consists of the following rules:
f(f(f(f(j, a), b), c), d) → f(f(a, b), f(f(a, d), c))
The set Q consists of the following terms:
f(f(f(f(j, x0), x1), x2), x3)
Using Dependency Pairs [1,13] we result in the following initial DP problem:
Q DP problem:
The TRS P consists of the following rules:
F(f(f(f(j, a), b), c), d) → F(a, d)
F(f(f(f(j, a), b), c), d) → F(f(a, b), f(f(a, d), c))
F(f(f(f(j, a), b), c), d) → F(f(a, d), c)
F(f(f(f(j, a), b), c), d) → F(a, b)
The TRS R consists of the following rules:
f(f(f(f(j, a), b), c), d) → f(f(a, b), f(f(a, d), c))
The set Q consists of the following terms:
f(f(f(f(j, x0), x1), x2), x3)
We have to consider all minimal (P,Q,R)-chains.
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
F(f(f(f(j, a), b), c), d) → F(a, d)
F(f(f(f(j, a), b), c), d) → F(f(a, b), f(f(a, d), c))
F(f(f(f(j, a), b), c), d) → F(f(a, d), c)
F(f(f(f(j, a), b), c), d) → F(a, b)
The TRS R consists of the following rules:
f(f(f(f(j, a), b), c), d) → f(f(a, b), f(f(a, d), c))
The set Q consists of the following terms:
f(f(f(f(j, x0), x1), x2), x3)
We have to consider all minimal (P,Q,R)-chains.