0.00/0.04 MAYBE 0.00/0.04 (ignored inputs)COMMENT Example 1 in extended version of [92] 0.00/0.04 Conditional Rewrite Rules: 0.00/0.04 [ f(c(?x),c(c(?y))) -> a(a(?x)) | c(f(?x,?y)) == c(a(b)), 0.00/0.04 f(c(c(c(?x))),?y) -> a(?y) | c(f(c(?x),c(c(?y)))) == c(a(a(b))), 0.00/0.04 h(b) -> b, 0.00/0.04 h(a(a(?x))) -> a(b) | h(?x) == b ] 0.00/0.04 Check whether all rules are type 3 0.00/0.04 OK 0.00/0.04 Check whether the input is deterministic 0.00/0.04 OK 0.00/0.04 Result of unraveling: 0.00/0.04 [ f(c(?x),c(c(?y))) -> U0(c(f(?x,?y)),?x,?y), 0.00/0.04 U0(c(a(b)),?x,?y) -> a(a(?x)), 0.00/0.04 f(c(c(c(?x))),?y) -> U1(c(f(c(?x),c(c(?y)))),?x,?y), 0.00/0.04 U1(c(a(a(b))),?x,?y) -> a(?y), 0.00/0.04 h(b) -> b, 0.00/0.04 h(a(a(?x))) -> U2(h(?x),?x), 0.00/0.04 U2(b,?x) -> a(b) ] 0.00/0.04 Check whether U(R) is terminating 0.00/0.04 OK 0.00/0.04 Check whether the input is weakly left-linear 0.00/0.04 OK 0.00/0.04 Check whether U(R) is confluent 0.00/0.04 U(R) is not confluent 0.00/0.04 Conditional critical pairs (CCPs): 0.00/0.04 [ a(c(c(?y))) = a(a(c(c(?x_1)))) | c(f(c(?x_1),c(c(c(c(?y)))))) == c(a(a(b))),c(f(c(c(?x_1)),?y)) == c(a(b)), 0.00/0.04 a(a(c(c(?x_1)))) = a(c(c(?y))) | c(f(c(c(?x_1)),?y)) == c(a(b)),c(f(c(?x_1),c(c(c(c(?y)))))) == c(a(a(b))) ] 0.00/0.04 Check whether the input is almost orthogonale 0.00/0.04 not almost orthogonal 0.00/0.04 OK 0.00/0.04 Check whether the input is absolutely irreducible 0.00/0.04 OK 0.00/0.04 Check whether all CCPs are joinable 0.00/0.04 Some ccp may be feasible but not joinable 0.00/0.04 [ a(c(c(?y))) = a(a(c(c(?x_1)))) | c(f(c(?x_1),c(c(c(c(?y)))))) == c(a(a(b))),c(f(c(c(?x_1)),?y)) == c(a(b)), 0.00/0.04 a(a(c(c(?x_1)))) = a(c(c(?y))) | c(f(c(c(?x_1)),?y)) == c(a(b)),c(f(c(?x_1),c(c(c(c(?y)))))) == c(a(a(b))) ] 0.00/0.04 /export/starexec/sandbox/benchmark/theBenchmark.trs: Failure(unknown CR) 0.00/0.04 (9 msec.) 0.00/0.04 EOF