(0) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
g(f(x, y), z) → f(x, g(y, z))
g(h(x, y), z) → g(x, f(y, z))
g(x, h(y, z)) → h(g(x, y), z)
Q is empty.
(1) QTRSRRRProof (EQUIVALENT transformation)
Used ordering:
Polynomial interpretation [POLO]:
POL(f(x1, x2)) = x1 + x2
POL(g(x1, x2)) = x1 + x2
POL(h(x1, x2)) = 1 + x1 + x2
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
g(h(x, y), z) → g(x, f(y, z))
(2) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
g(f(x, y), z) → f(x, g(y, z))
g(x, h(y, z)) → h(g(x, y), z)
Q is empty.
(3) QTRSRRRProof (EQUIVALENT transformation)
Used ordering:
Polynomial interpretation [POLO]:
POL(f(x1, x2)) = 1 + x1 + x2
POL(g(x1, x2)) = 2 + 2·x1 + 2·x2
POL(h(x1, x2)) = 1 + x1 + x2
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
g(f(x, y), z) → f(x, g(y, z))
g(x, h(y, z)) → h(g(x, y), z)
(4) Obligation:
Q restricted rewrite system:
R is empty.
Q is empty.
(5) RisEmptyProof (EQUIVALENT transformation)
The TRS R is empty. Hence, termination is trivially proven.
(6) TRUE
(7) RisEmptyProof (EQUIVALENT transformation)
The TRS R is empty. Hence, termination is trivially proven.
(8) TRUE