0.00/0.00 NO 0.00/0.00 0.00/0.00 0.00/0.00 Succeeded in reading "/export/starexec/sandbox/benchmark/theBenchmark.trs". 0.00/0.00 (CONDITIONTYPE ORIENTED) 0.00/0.00 (VAR x z) 0.00/0.00 (RULES 0.00/0.00 f(k(z),a) -> g(x,x) | h(z) == x, x == b 0.00/0.00 f(k(a),h(a)) -> k(x) | a == x 0.00/0.00 k(x) -> h(x) 0.00/0.00 k(x) -> b 0.00/0.00 k(x) -> a 0.00/0.00 a -> b 0.00/0.00 g(x,x) -> a 0.00/0.00 ) 0.00/0.00 (COMMENT submitted by: Florian Messner used by COPS #1145) 0.00/0.00 0.00/0.00 No "->="-rules. 0.00/0.00 0.00/0.00 Decomposed conditions if possible. 0.00/0.00 (CONDITIONTYPE ORIENTED) 0.00/0.00 (VAR x z) 0.00/0.00 (RULES 0.00/0.00 f(k(z),a) -> g(x,x) | h(z) == x, x == b 0.00/0.00 f(k(a),h(a)) -> k(x) | a == x 0.00/0.00 k(x) -> h(x) 0.00/0.00 k(x) -> b 0.00/0.00 k(x) -> a 0.00/0.00 a -> b 0.00/0.00 g(x,x) -> a 0.00/0.00 ) 0.00/0.00 (COMMENT submitted by: Florian Messner used by COPS #1145) 0.00/0.00 0.00/0.00 Removed infeasible rules as much as possible. 0.00/0.00 (CONDITIONTYPE ORIENTED) 0.00/0.00 (VAR x z) 0.00/0.00 (RULES 0.00/0.00 f(k(z),a) -> g(x,x) | h(z) == x, x == b 0.00/0.00 f(k(a),h(a)) -> k(x) | a == x 0.00/0.00 k(x) -> h(x) 0.00/0.00 k(x) -> b 0.00/0.00 k(x) -> a 0.00/0.00 a -> b 0.00/0.00 g(x,x) -> a 0.00/0.00 ) 0.00/0.00 (COMMENT submitted by: Florian Messner used by COPS #1145) 0.00/0.00 0.00/0.00 Try to disprove confluence of the following (C)TRS: 0.00/0.00 (CONDITIONTYPE ORIENTED) 0.00/0.00 (VAR x z) 0.00/0.00 (RULES 0.00/0.00 f(k(z),a) -> g(x,x) | h(z) == x, x == b 0.00/0.00 f(k(a),h(a)) -> k(x) | a == x 0.00/0.00 k(x) -> h(x) 0.00/0.00 k(x) -> b 0.00/0.00 k(x) -> a 0.00/0.00 a -> b 0.00/0.00 g(x,x) -> a 0.00/0.00 ) 0.00/0.00 (COMMENT submitted by: Florian Messner used by COPS #1145) 0.00/0.00 0.00/0.00 Succeeded in disproving confluence. 0.00/0.00 0.00/0.00 Disproved via the following (C)TRS: 0.00/0.00 (CONDITIONTYPE ORIENTED) 0.00/0.00 (VAR x z) 0.00/0.00 (RULES 0.00/0.00 f(k(z),a) -> g(x,x) | h(z) == x, x == b 0.00/0.00 f(k(a),h(a)) -> k(x) | a == x 0.00/0.00 k(x) -> h(x) 0.00/0.00 k(x) -> b 0.00/0.00 k(x) -> a 0.00/0.00 a -> b 0.00/0.00 g(x,x) -> a 0.00/0.00 ) 0.00/0.00 (COMMENT submitted by: Florian Messner used by COPS #1145) 0.00/0.00 0.00/0.00 NO 0.00/0.00 EOF