(0) Obligation:
Relative term rewrite system:
The relative TRS consists of the following R rules:
f(s(x), y) → f(-(s(x), y), y)
The relative TRS consists of the following S rules:
+(s(x), y) → s(+(x, y))
-(0, y) → 0
-(s(x), s(y)) → -(x, y)
-(x, 0) → x
f(x, y) → f(x, +(x, y))
+(0, y) → y
(1) RelTRSLoopFinderProof (COMPLETE transformation)
The following loop was found:
---------- Loop: ----------
f(-(s(x), 0), 0) → f(s(x), 0) with rule -(x', 0) → x' at position [0] and matcher [x' / s(x)]
f(s(x), 0) → f(-(s(x), 0), 0) with rule f(s(x'), y) → f(-(s(x'), y), y) at position [] and matcher [x' / x, y / 0]
Now an instance of the first term with Matcher [ ] occurs in the last term at position [].
Context: []
Therefore, the relative TRS problem does not terminate.
(2) NO