42.45/11.82 NO 42.45/11.83 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 42.45/11.83 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 42.45/11.83 42.45/11.83 42.45/11.83 Termination of the given RelTRS could be disproven: 42.45/11.83 42.45/11.83 (0) RelTRS 42.45/11.83 (1) RelTRSLoopFinderProof [COMPLETE, 5591 ms] 42.45/11.83 (2) NO 42.45/11.83 42.45/11.83 42.45/11.83 ---------------------------------------- 42.45/11.83 42.45/11.83 (0) 42.45/11.83 Obligation: 42.45/11.83 Relative term rewrite system: 42.45/11.83 The relative TRS consists of the following R rules: 42.45/11.83 42.45/11.83 top(ok(U(x, y))) -> top(check(D(x, y))) 42.45/11.83 D(x, B) -> U(x, B) 42.45/11.83 F(x, U(O(y), z)) -> U(x, F(y, z)) 42.45/11.83 F(x, U(N(y), z)) -> U(x, F(y, z)) 42.45/11.83 D(O(x), F(y, z)) -> F(x, D(y, z)) 42.45/11.83 D(N(x), F(y, z)) -> F(x, D(y, z)) 42.45/11.83 F(x, U(E, y)) -> U(x, F(E, y)) 42.45/11.83 D(E, F(x, y)) -> F(E, D(x, y)) 42.45/11.83 42.45/11.83 The relative TRS consists of the following S rules: 42.45/11.83 42.45/11.83 U(O(x), y) -> U(x, y) 42.45/11.83 U(N(x), y) -> U(x, y) 42.45/11.83 D(O(x), y) -> D(x, y) 42.45/11.83 D(N(x), y) -> D(x, y) 42.45/11.83 E -> N(E) 42.45/11.83 check(O(x)) -> ok(O(x)) 42.45/11.83 check(U(x, y)) -> U(check(x), y) 42.45/11.83 check(U(x, y)) -> U(x, check(y)) 42.45/11.83 check(D(x, y)) -> D(check(x), y) 42.45/11.83 check(D(x, y)) -> D(x, check(y)) 42.45/11.83 check(F(x, y)) -> F(check(x), y) 42.45/11.83 check(F(x, y)) -> F(x, check(y)) 42.45/11.83 check(O(x)) -> O(check(x)) 42.45/11.83 check(N(x)) -> N(check(x)) 42.45/11.83 U(ok(x), y) -> ok(U(x, y)) 42.45/11.83 U(x, ok(y)) -> ok(U(x, y)) 42.45/11.83 D(ok(x), y) -> ok(D(x, y)) 42.45/11.83 D(x, ok(y)) -> ok(D(x, y)) 42.45/11.83 F(ok(x), y) -> ok(F(x, y)) 42.45/11.83 F(x, ok(y)) -> ok(F(x, y)) 42.45/11.83 O(ok(x)) -> ok(O(x)) 42.45/11.83 N(ok(x)) -> ok(N(x)) 42.45/11.83 42.45/11.83 42.45/11.83 ---------------------------------------- 42.45/11.83 42.45/11.83 (1) RelTRSLoopFinderProof (COMPLETE) 42.45/11.83 The following loop was found: 42.45/11.83 42.45/11.83 ---------- Loop: ---------- 42.45/11.83 42.45/11.83 top(check(D(O(x), B))) -> top(D(check(O(x)), B)) with rule check(D(x', y)) -> D(check(x'), y) at position [0] and matcher [x' / O(x), y / B] 42.45/11.83 42.45/11.83 top(D(check(O(x)), B)) -> top(D(ok(O(x)), B)) with rule check(O(x')) -> ok(O(x')) at position [0,0] and matcher [x' / x] 42.45/11.83 42.45/11.83 top(D(ok(O(x)), B)) -> top(U(ok(O(x)), B)) with rule D(x', B) -> U(x', B) at position [0] and matcher [x' / ok(O(x))] 42.45/11.83 42.45/11.83 top(U(ok(O(x)), B)) -> top(ok(U(O(x), B))) with rule U(ok(x'), y') -> ok(U(x', y')) at position [0] and matcher [x' / O(x), y' / B] 42.45/11.83 42.45/11.83 top(ok(U(O(x), B))) -> top(check(D(O(x), B))) with rule top(ok(U(x', y))) -> top(check(D(x', y))) at position [] and matcher [x' / O(x), y / B] 42.45/11.83 42.45/11.83 Now an instance of the first term with Matcher [ ] occurs in the last term at position []. 42.45/11.83 42.45/11.83 Context: [] 42.45/11.83 42.45/11.83 Therefore, the relative TRS problem does not terminate. 42.45/11.83 ---------------------------------------- 42.45/11.83 42.45/11.83 (2) 42.45/11.83 NO 42.59/11.87 EOF