(0) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
+(+(x, y), z) → +(x, +(y, z))
+(f(x), f(y)) → f(+(x, y))
+(f(x), +(f(y), z)) → +(f(+(x, y)), z)
Q is empty.
(1) DependencyPairsProof (EQUIVALENT transformation)
Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem.
(2) Obligation:
Q DP problem:
The TRS P consists of the following rules:
+1(+(x, y), z) → +1(x, +(y, z))
+1(+(x, y), z) → +1(y, z)
+1(f(x), f(y)) → +1(x, y)
+1(f(x), +(f(y), z)) → +1(f(+(x, y)), z)
+1(f(x), +(f(y), z)) → +1(x, y)
The TRS R consists of the following rules:
+(+(x, y), z) → +(x, +(y, z))
+(f(x), f(y)) → f(+(x, y))
+(f(x), +(f(y), z)) → +(f(+(x, y)), z)
Q is empty.
We have to consider all minimal (P,Q,R)-chains.