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:
+2(x, +2(y, z)) -> +2(+2(x, y), z)
*2(x, +2(y, z)) -> +2(*2(x, y), *2(x, z))
+2(+2(x, *2(y, z)), *2(y, u)) -> +2(x, *2(y, +2(z, u)))
Q is empty.
↳ QTRS
↳ DependencyPairsProof
Q restricted rewrite system:
The TRS R consists of the following rules:
+2(x, +2(y, z)) -> +2(+2(x, y), z)
*2(x, +2(y, z)) -> +2(*2(x, y), *2(x, z))
+2(+2(x, *2(y, z)), *2(y, u)) -> +2(x, *2(y, +2(z, u)))
Q is empty.
Using Dependency Pairs [1,13] we result in the following initial DP problem:
Q DP problem:
The TRS P consists of the following rules:
+12(+2(x, *2(y, z)), *2(y, u)) -> +12(z, u)
+12(+2(x, *2(y, z)), *2(y, u)) -> *12(y, +2(z, u))
*12(x, +2(y, z)) -> +12(*2(x, y), *2(x, z))
+12(+2(x, *2(y, z)), *2(y, u)) -> +12(x, *2(y, +2(z, u)))
*12(x, +2(y, z)) -> *12(x, z)
*12(x, +2(y, z)) -> *12(x, y)
+12(x, +2(y, z)) -> +12(x, y)
+12(x, +2(y, z)) -> +12(+2(x, y), z)
The TRS R consists of the following rules:
+2(x, +2(y, z)) -> +2(+2(x, y), z)
*2(x, +2(y, z)) -> +2(*2(x, y), *2(x, z))
+2(+2(x, *2(y, z)), *2(y, u)) -> +2(x, *2(y, +2(z, u)))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
↳ QTRS
↳ DependencyPairsProof
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
+12(+2(x, *2(y, z)), *2(y, u)) -> +12(z, u)
+12(+2(x, *2(y, z)), *2(y, u)) -> *12(y, +2(z, u))
*12(x, +2(y, z)) -> +12(*2(x, y), *2(x, z))
+12(+2(x, *2(y, z)), *2(y, u)) -> +12(x, *2(y, +2(z, u)))
*12(x, +2(y, z)) -> *12(x, z)
*12(x, +2(y, z)) -> *12(x, y)
+12(x, +2(y, z)) -> +12(x, y)
+12(x, +2(y, z)) -> +12(+2(x, y), z)
The TRS R consists of the following rules:
+2(x, +2(y, z)) -> +2(+2(x, y), z)
*2(x, +2(y, z)) -> +2(*2(x, y), *2(x, z))
+2(+2(x, *2(y, z)), *2(y, u)) -> +2(x, *2(y, +2(z, u)))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.