59.82/16.04 YES 60.02/16.09 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 60.02/16.09 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 60.02/16.09 60.02/16.09 60.02/16.09 Termination w.r.t. Q of the given QTRS could be proven: 60.02/16.09 60.02/16.09 (0) QTRS 60.02/16.09 (1) QTRS Reverse [EQUIVALENT, 0 ms] 60.02/16.09 (2) QTRS 60.02/16.09 (3) DependencyPairsProof [EQUIVALENT, 1107 ms] 60.02/16.09 (4) QDP 60.02/16.09 (5) DependencyGraphProof [EQUIVALENT, 0 ms] 60.02/16.09 (6) QDP 60.02/16.09 (7) QDPOrderProof [EQUIVALENT, 341 ms] 60.02/16.09 (8) QDP 60.02/16.09 (9) UsableRulesProof [EQUIVALENT, 0 ms] 60.02/16.09 (10) QDP 60.02/16.09 (11) QDPSizeChangeProof [EQUIVALENT, 0 ms] 60.02/16.09 (12) YES 60.02/16.09 60.02/16.09 60.02/16.09 ---------------------------------------- 60.02/16.09 60.02/16.09 (0) 60.02/16.09 Obligation: 60.02/16.09 Q restricted rewrite system: 60.02/16.09 The TRS R consists of the following rules: 60.02/16.09 60.02/16.09 0(1(0(1(x1)))) -> 0(0(2(1(3(1(x1)))))) 60.02/16.09 0(1(0(1(x1)))) -> 2(1(0(2(0(1(x1)))))) 60.02/16.09 0(1(0(1(x1)))) -> 2(1(3(1(0(0(x1)))))) 60.02/16.09 4(1(0(1(x1)))) -> 1(0(4(2(1(x1))))) 60.02/16.09 4(1(0(1(x1)))) -> 4(1(0(2(1(x1))))) 60.02/16.09 4(1(0(1(x1)))) -> 0(2(1(3(4(1(x1)))))) 60.02/16.09 4(1(0(1(x1)))) -> 0(4(2(1(3(1(x1)))))) 60.02/16.09 4(1(0(1(x1)))) -> 1(0(2(4(1(3(x1)))))) 60.02/16.09 4(1(0(1(x1)))) -> 1(0(4(2(2(1(x1)))))) 60.02/16.09 4(1(0(1(x1)))) -> 1(0(4(5(2(1(x1)))))) 60.02/16.09 4(1(0(1(x1)))) -> 4(0(2(1(3(1(x1)))))) 60.02/16.09 4(1(0(1(x1)))) -> 4(1(0(2(1(3(x1)))))) 60.02/16.09 4(1(0(1(x1)))) -> 4(1(3(0(2(1(x1)))))) 60.02/16.09 4(1(1(1(x1)))) -> 4(1(3(1(3(1(x1)))))) 60.02/16.09 4(3(0(1(x1)))) -> 0(2(1(3(4(x1))))) 60.02/16.09 4(3(0(1(x1)))) -> 0(2(4(1(3(x1))))) 60.02/16.09 4(3(0(1(x1)))) -> 0(4(2(1(3(x1))))) 60.02/16.09 4(3(0(1(x1)))) -> 3(0(4(2(1(x1))))) 60.02/16.09 4(3(0(1(x1)))) -> 3(4(0(2(1(x1))))) 60.02/16.09 4(3(0(1(x1)))) -> 4(0(2(1(3(x1))))) 60.02/16.09 4(3(0(1(x1)))) -> 4(3(0(2(1(x1))))) 60.02/16.09 4(3(0(1(x1)))) -> 0(2(1(3(3(4(x1)))))) 60.02/16.09 4(3(0(1(x1)))) -> 0(2(1(3(4(3(x1)))))) 60.02/16.09 4(3(0(1(x1)))) -> 0(2(4(1(3(3(x1)))))) 60.02/16.09 4(3(0(1(x1)))) -> 0(4(2(2(1(3(x1)))))) 60.02/16.09 4(3(0(1(x1)))) -> 0(4(5(2(1(3(x1)))))) 60.02/16.09 4(3(0(1(x1)))) -> 1(0(2(1(3(4(x1)))))) 60.02/16.09 4(3(0(1(x1)))) -> 1(0(2(4(1(3(x1)))))) 60.02/16.09 4(3(0(1(x1)))) -> 1(0(4(2(1(3(x1)))))) 60.02/16.09 4(3(0(1(x1)))) -> 1(3(0(4(2(1(x1)))))) 60.02/16.09 4(3(0(1(x1)))) -> 3(0(4(5(2(1(x1)))))) 60.02/16.09 4(3(0(1(x1)))) -> 3(1(0(4(2(1(x1)))))) 60.02/16.09 4(3(0(1(x1)))) -> 3(3(4(0(2(1(x1)))))) 60.02/16.09 4(3(0(1(x1)))) -> 3(4(0(2(1(3(x1)))))) 60.02/16.09 4(3(0(1(x1)))) -> 3(4(0(2(2(1(x1)))))) 60.02/16.09 4(3(0(1(x1)))) -> 3(4(0(5(2(1(x1)))))) 60.02/16.09 4(3(0(1(x1)))) -> 3(4(1(0(2(1(x1)))))) 60.02/16.09 4(3(0(1(x1)))) -> 3(4(3(0(2(1(x1)))))) 60.02/16.09 4(3(0(1(x1)))) -> 4(3(0(2(1(3(x1)))))) 60.02/16.09 4(3(0(1(x1)))) -> 4(3(0(5(2(1(x1)))))) 60.02/16.09 4(3(0(1(x1)))) -> 4(3(1(0(2(1(x1)))))) 60.02/16.09 4(3(0(1(x1)))) -> 4(3(3(0(2(1(x1)))))) 60.02/16.09 4(5(1(1(x1)))) -> 4(5(2(1(1(x1))))) 60.02/16.09 4(5(1(1(x1)))) -> 4(2(5(2(1(1(x1)))))) 60.02/16.09 4(5(1(1(x1)))) -> 4(5(2(1(3(1(x1)))))) 60.02/16.09 4(5(1(1(x1)))) -> 4(5(2(2(1(1(x1)))))) 60.02/16.09 4(5(1(1(x1)))) -> 4(5(5(2(1(1(x1)))))) 60.02/16.09 0(0(1(0(1(x1))))) -> 0(0(1(0(2(1(x1)))))) 60.02/16.09 0(0(3(1(1(x1))))) -> 2(1(3(1(0(0(x1)))))) 60.02/16.09 0(0(5(1(1(x1))))) -> 5(0(0(2(1(1(x1)))))) 60.02/16.09 0(4(1(0(1(x1))))) -> 2(1(0(4(0(1(x1)))))) 60.02/16.09 0(4(3(0(1(x1))))) -> 0(0(2(1(3(4(x1)))))) 60.02/16.09 0(4(3(0(1(x1))))) -> 0(4(3(0(2(1(x1)))))) 60.02/16.09 0(4(3(0(1(x1))))) -> 2(3(1(0(4(0(x1)))))) 60.02/16.09 0(4(3(1(1(x1))))) -> 2(1(4(1(3(0(x1)))))) 60.02/16.09 0(4(3(1(1(x1))))) -> 4(2(0(3(1(1(x1)))))) 60.02/16.09 0(4(5(1(1(x1))))) -> 4(0(1(5(2(1(x1)))))) 60.02/16.09 0(4(5(1(1(x1))))) -> 5(2(1(4(0(1(x1)))))) 60.02/16.09 4(0(3(0(1(x1))))) -> 0(0(4(2(1(3(x1)))))) 60.02/16.09 4(0(3(0(1(x1))))) -> 2(0(4(0(1(3(x1)))))) 60.02/16.09 4(0(3(0(1(x1))))) -> 2(0(4(0(3(1(x1)))))) 60.02/16.09 4(1(0(1(1(x1))))) -> 1(0(4(2(1(1(x1)))))) 60.02/16.09 4(1(1(0(1(x1))))) -> 4(1(0(2(1(1(x1)))))) 60.02/16.09 4(1(2(0(1(x1))))) -> 0(4(2(1(3(1(x1)))))) 60.02/16.09 4(1(2(0(1(x1))))) -> 1(0(2(4(1(3(x1)))))) 60.02/16.09 4(1(2(0(1(x1))))) -> 4(0(2(2(1(1(x1)))))) 60.02/16.09 4(1(2(0(1(x1))))) -> 4(1(0(2(2(1(x1)))))) 60.02/16.09 4(1(3(0(1(x1))))) -> 4(1(3(0(2(1(x1)))))) 60.02/16.09 4(1(5(0(1(x1))))) -> 1(1(5(0(4(2(x1)))))) 60.02/16.09 4(1(5(1(1(x1))))) -> 1(4(5(2(1(1(x1)))))) 60.02/16.09 4(3(0(1(1(x1))))) -> 1(3(0(2(1(4(x1)))))) 60.02/16.09 4(3(0(1(1(x1))))) -> 1(3(1(4(0(2(x1)))))) 60.02/16.09 4(3(0(1(1(x1))))) -> 1(3(1(4(2(0(x1)))))) 60.02/16.09 4(3(0(1(1(x1))))) -> 3(1(0(2(4(1(x1)))))) 60.02/16.09 4(3(0(1(1(x1))))) -> 4(3(1(1(0(2(x1)))))) 60.02/16.09 4(3(1(0(1(x1))))) -> 0(4(2(1(3(1(x1)))))) 60.02/16.09 4(3(1(0(1(x1))))) -> 1(3(4(0(2(1(x1)))))) 60.02/16.09 4(3(2(0(1(x1))))) -> 3(4(0(2(2(1(x1)))))) 60.02/16.09 4(3(2(0(1(x1))))) -> 3(4(0(5(2(1(x1)))))) 60.02/16.09 4(3(2(0(1(x1))))) -> 4(0(2(1(3(1(x1)))))) 60.02/16.09 4(3(2(0(1(x1))))) -> 4(3(0(2(1(3(x1)))))) 60.02/16.09 4(3(2(1(1(x1))))) -> 1(3(1(2(4(2(x1)))))) 60.02/16.09 4(3(2(1(1(x1))))) -> 1(3(1(4(5(2(x1)))))) 60.02/16.09 4(3(2(1(1(x1))))) -> 3(1(3(4(1(2(x1)))))) 60.02/16.09 4(3(2(1(1(x1))))) -> 4(1(3(1(2(2(x1)))))) 60.02/16.09 4(3(2(1(1(x1))))) -> 4(1(3(3(1(2(x1)))))) 60.02/16.09 4(3(3(0(1(x1))))) -> 4(3(3(0(2(1(x1)))))) 60.02/16.09 4(3(4(0(1(x1))))) -> 3(4(0(4(2(1(x1)))))) 60.02/16.09 4(3(4(0(1(x1))))) -> 4(4(0(2(1(3(x1)))))) 60.02/16.09 4(3(5(0(1(x1))))) -> 0(5(2(3(1(4(x1)))))) 60.02/16.09 4(3(5(0(1(x1))))) -> 1(3(0(2(5(4(x1)))))) 60.02/16.09 4(3(5(0(1(x1))))) -> 1(3(0(4(2(5(x1)))))) 60.02/16.09 4(3(5(0(1(x1))))) -> 1(3(4(0(5(2(x1)))))) 60.02/16.09 4(3(5(0(1(x1))))) -> 3(1(0(4(2(5(x1)))))) 60.02/16.09 4(3(5(0(1(x1))))) -> 3(1(5(0(4(2(x1)))))) 60.02/16.09 4(3(5(0(1(x1))))) -> 3(4(0(2(1(5(x1)))))) 60.02/16.09 4(3(5(0(1(x1))))) -> 3(4(1(5(0(2(x1)))))) 60.02/16.09 4(3(5(0(1(x1))))) -> 3(5(1(0(4(2(x1)))))) 60.02/16.09 4(3(5(0(1(x1))))) -> 4(3(0(2(1(5(x1)))))) 60.02/16.09 4(3(5(0(1(x1))))) -> 5(1(3(4(0(2(x1)))))) 60.02/16.09 4(3(5(1(1(x1))))) -> 1(4(5(2(1(3(x1)))))) 60.02/16.09 4(3(5(1(1(x1))))) -> 3(1(1(5(4(2(x1)))))) 60.02/16.09 4(3(5(1(1(x1))))) -> 3(1(4(5(2(1(x1)))))) 60.02/16.09 4(3(5(1(1(x1))))) -> 4(1(3(1(3(5(x1)))))) 60.02/16.09 4(3(5(1(1(x1))))) -> 4(1(5(2(1(3(x1)))))) 60.02/16.09 4(3(5(1(1(x1))))) -> 4(3(1(5(2(1(x1)))))) 60.02/16.09 4(4(1(0(1(x1))))) -> 4(4(1(0(2(1(x1)))))) 60.02/16.09 4(4(3(0(1(x1))))) -> 0(4(4(2(1(3(x1)))))) 60.02/16.09 4(4(3(0(1(x1))))) -> 4(0(2(1(3(4(x1)))))) 60.02/16.09 4(4(3(0(1(x1))))) -> 4(3(4(0(2(1(x1)))))) 60.02/16.09 4(4(3(0(1(x1))))) -> 4(4(3(0(2(1(x1)))))) 60.02/16.09 4(5(1(0(1(x1))))) -> 0(5(1(3(4(1(x1)))))) 60.02/16.09 4(5(1(0(1(x1))))) -> 0(5(4(1(3(1(x1)))))) 60.02/16.09 4(5(1(0(1(x1))))) -> 1(0(4(5(2(1(x1)))))) 60.02/16.09 4(5(1(0(1(x1))))) -> 4(0(5(2(1(1(x1)))))) 60.02/16.09 4(5(1(0(1(x1))))) -> 4(5(1(0(2(1(x1)))))) 60.02/16.09 4(5(1(0(1(x1))))) -> 5(1(0(2(4(1(x1)))))) 60.02/16.09 4(5(1(0(1(x1))))) -> 5(4(1(0(2(1(x1)))))) 60.02/16.09 4(5(1(1(1(x1))))) -> 4(5(2(1(1(1(x1)))))) 60.02/16.09 4(5(3(0(1(x1))))) -> 0(2(1(3(4(5(x1)))))) 60.02/16.09 4(5(3(0(1(x1))))) -> 0(5(2(1(3(4(x1)))))) 60.02/16.09 4(5(3(0(1(x1))))) -> 0(5(2(4(3(1(x1)))))) 60.02/16.09 4(5(3(0(1(x1))))) -> 0(5(4(2(1(3(x1)))))) 60.02/16.09 4(5(3(0(1(x1))))) -> 1(0(5(1(3(4(x1)))))) 60.02/16.09 4(5(3(0(1(x1))))) -> 1(5(0(3(3(4(x1)))))) 60.02/16.09 4(5(3(0(1(x1))))) -> 2(1(4(5(0(3(x1)))))) 60.02/16.09 4(5(3(0(1(x1))))) -> 2(4(1(3(5(0(x1)))))) 60.02/16.09 4(5(3(0(1(x1))))) -> 3(0(4(5(2(1(x1)))))) 60.02/16.09 4(5(3(0(1(x1))))) -> 4(0(3(1(5(2(x1)))))) 60.02/16.09 4(5(3(0(1(x1))))) -> 4(0(3(3(5(1(x1)))))) 60.02/16.09 4(5(3(0(1(x1))))) -> 4(0(5(4(1(3(x1)))))) 60.02/16.09 4(5(3(0(1(x1))))) -> 4(1(3(5(0(3(x1)))))) 60.02/16.09 4(5(3(0(1(x1))))) -> 4(1(3(5(5(0(x1)))))) 60.02/16.09 4(5(3(0(1(x1))))) -> 4(2(5(0(3(1(x1)))))) 60.02/16.09 4(5(3(0(1(x1))))) -> 4(5(2(0(3(1(x1)))))) 60.02/16.09 4(5(3(0(1(x1))))) -> 5(0(3(1(4(1(x1)))))) 60.02/16.09 4(5(3(0(1(x1))))) -> 5(0(3(4(4(1(x1)))))) 60.02/16.09 4(5(3(0(1(x1))))) -> 5(1(3(0(3(4(x1)))))) 60.02/16.09 4(5(3(0(1(x1))))) -> 5(2(1(3(4(0(x1)))))) 60.02/16.09 4(5(3(0(1(x1))))) -> 5(2(4(1(3(0(x1)))))) 60.02/16.09 4(5(3(0(1(x1))))) -> 5(3(0(4(2(1(x1)))))) 60.02/16.09 4(5(3(0(1(x1))))) -> 5(4(1(3(0(1(x1)))))) 60.02/16.09 4(5(3(0(1(x1))))) -> 5(4(1(3(2(0(x1)))))) 60.02/16.09 4(5(3(0(1(x1))))) -> 5(4(3(0(2(1(x1)))))) 60.02/16.09 4(5(3(1(1(x1))))) -> 2(4(1(3(1(5(x1)))))) 60.02/16.09 4(5(3(1(1(x1))))) -> 4(5(2(1(3(1(x1)))))) 60.02/16.09 4(5(3(1(1(x1))))) -> 5(1(3(4(1(2(x1)))))) 60.02/16.09 4(5(3(1(1(x1))))) -> 5(2(1(4(1(3(x1)))))) 60.02/16.09 4(5(3(1(1(x1))))) -> 5(4(2(1(3(1(x1)))))) 60.02/16.09 4(5(5(1(1(x1))))) -> 5(5(2(1(1(4(x1)))))) 60.02/16.09 4(5(5(1(1(x1))))) -> 5(5(2(4(1(1(x1)))))) 60.02/16.09 60.02/16.09 Q is empty. 60.02/16.09 60.02/16.09 ---------------------------------------- 60.02/16.09 60.02/16.09 (1) QTRS Reverse (EQUIVALENT) 60.02/16.09 We applied the QTRS Reverse Processor [REVERSE]. 60.02/16.09 ---------------------------------------- 60.02/16.09 60.02/16.09 (2) 60.02/16.09 Obligation: 60.02/16.09 Q restricted rewrite system: 60.02/16.09 The TRS R consists of the following rules: 60.02/16.09 60.02/16.09 1(0(1(0(x1)))) -> 1(3(1(2(0(0(x1)))))) 60.02/16.09 1(0(1(0(x1)))) -> 1(0(2(0(1(2(x1)))))) 60.02/16.09 1(0(1(0(x1)))) -> 0(0(1(3(1(2(x1)))))) 60.02/16.09 1(0(1(4(x1)))) -> 1(2(4(0(1(x1))))) 60.02/16.09 1(0(1(4(x1)))) -> 1(2(0(1(4(x1))))) 60.02/16.09 1(0(1(4(x1)))) -> 1(4(3(1(2(0(x1)))))) 60.02/16.09 1(0(1(4(x1)))) -> 1(3(1(2(4(0(x1)))))) 60.02/16.09 1(0(1(4(x1)))) -> 3(1(4(2(0(1(x1)))))) 60.02/16.09 1(0(1(4(x1)))) -> 1(2(2(4(0(1(x1)))))) 60.02/16.09 1(0(1(4(x1)))) -> 1(2(5(4(0(1(x1)))))) 60.02/16.09 1(0(1(4(x1)))) -> 1(3(1(2(0(4(x1)))))) 60.02/16.09 1(0(1(4(x1)))) -> 3(1(2(0(1(4(x1)))))) 60.02/16.09 1(0(1(4(x1)))) -> 1(2(0(3(1(4(x1)))))) 60.02/16.09 1(1(1(4(x1)))) -> 1(3(1(3(1(4(x1)))))) 60.02/16.09 1(0(3(4(x1)))) -> 4(3(1(2(0(x1))))) 60.02/16.09 1(0(3(4(x1)))) -> 3(1(4(2(0(x1))))) 60.02/16.09 1(0(3(4(x1)))) -> 3(1(2(4(0(x1))))) 60.02/16.09 1(0(3(4(x1)))) -> 1(2(4(0(3(x1))))) 60.02/16.09 1(0(3(4(x1)))) -> 1(2(0(4(3(x1))))) 60.02/16.09 1(0(3(4(x1)))) -> 3(1(2(0(4(x1))))) 60.02/16.09 1(0(3(4(x1)))) -> 1(2(0(3(4(x1))))) 60.02/16.09 1(0(3(4(x1)))) -> 4(3(3(1(2(0(x1)))))) 60.02/16.09 1(0(3(4(x1)))) -> 3(4(3(1(2(0(x1)))))) 60.02/16.09 1(0(3(4(x1)))) -> 3(3(1(4(2(0(x1)))))) 60.02/16.09 1(0(3(4(x1)))) -> 3(1(2(2(4(0(x1)))))) 60.02/16.09 1(0(3(4(x1)))) -> 3(1(2(5(4(0(x1)))))) 60.02/16.09 1(0(3(4(x1)))) -> 4(3(1(2(0(1(x1)))))) 60.02/16.09 1(0(3(4(x1)))) -> 3(1(4(2(0(1(x1)))))) 60.02/16.09 1(0(3(4(x1)))) -> 3(1(2(4(0(1(x1)))))) 60.02/16.09 1(0(3(4(x1)))) -> 1(2(4(0(3(1(x1)))))) 60.02/16.09 1(0(3(4(x1)))) -> 1(2(5(4(0(3(x1)))))) 60.02/16.09 1(0(3(4(x1)))) -> 1(2(4(0(1(3(x1)))))) 60.02/16.09 1(0(3(4(x1)))) -> 1(2(0(4(3(3(x1)))))) 60.02/16.09 1(0(3(4(x1)))) -> 3(1(2(0(4(3(x1)))))) 60.02/16.09 1(0(3(4(x1)))) -> 1(2(2(0(4(3(x1)))))) 60.02/16.09 1(0(3(4(x1)))) -> 1(2(5(0(4(3(x1)))))) 60.02/16.09 1(0(3(4(x1)))) -> 1(2(0(1(4(3(x1)))))) 60.02/16.09 1(0(3(4(x1)))) -> 1(2(0(3(4(3(x1)))))) 60.02/16.09 1(0(3(4(x1)))) -> 3(1(2(0(3(4(x1)))))) 60.02/16.09 1(0(3(4(x1)))) -> 1(2(5(0(3(4(x1)))))) 60.02/16.09 1(0(3(4(x1)))) -> 1(2(0(1(3(4(x1)))))) 60.02/16.09 1(0(3(4(x1)))) -> 1(2(0(3(3(4(x1)))))) 60.02/16.09 1(1(5(4(x1)))) -> 1(1(2(5(4(x1))))) 60.02/16.09 1(1(5(4(x1)))) -> 1(1(2(5(2(4(x1)))))) 60.02/16.09 1(1(5(4(x1)))) -> 1(3(1(2(5(4(x1)))))) 60.02/16.09 1(1(5(4(x1)))) -> 1(1(2(2(5(4(x1)))))) 60.02/16.09 1(1(5(4(x1)))) -> 1(1(2(5(5(4(x1)))))) 60.02/16.09 1(0(1(0(0(x1))))) -> 1(2(0(1(0(0(x1)))))) 60.02/16.09 1(1(3(0(0(x1))))) -> 0(0(1(3(1(2(x1)))))) 60.02/16.09 1(1(5(0(0(x1))))) -> 1(1(2(0(0(5(x1)))))) 60.02/16.09 1(0(1(4(0(x1))))) -> 1(0(4(0(1(2(x1)))))) 60.02/16.09 1(0(3(4(0(x1))))) -> 4(3(1(2(0(0(x1)))))) 60.02/16.09 1(0(3(4(0(x1))))) -> 1(2(0(3(4(0(x1)))))) 60.02/16.09 1(0(3(4(0(x1))))) -> 0(4(0(1(3(2(x1)))))) 60.02/16.09 1(1(3(4(0(x1))))) -> 0(3(1(4(1(2(x1)))))) 60.02/16.09 1(1(3(4(0(x1))))) -> 1(1(3(0(2(4(x1)))))) 60.02/16.09 1(1(5(4(0(x1))))) -> 1(2(5(1(0(4(x1)))))) 60.02/16.09 1(1(5(4(0(x1))))) -> 1(0(4(1(2(5(x1)))))) 60.02/16.09 1(0(3(0(4(x1))))) -> 3(1(2(4(0(0(x1)))))) 60.02/16.09 1(0(3(0(4(x1))))) -> 3(1(0(4(0(2(x1)))))) 60.02/16.09 1(0(3(0(4(x1))))) -> 1(3(0(4(0(2(x1)))))) 60.02/16.09 1(1(0(1(4(x1))))) -> 1(1(2(4(0(1(x1)))))) 60.02/16.09 1(0(1(1(4(x1))))) -> 1(1(2(0(1(4(x1)))))) 60.02/16.09 1(0(2(1(4(x1))))) -> 1(3(1(2(4(0(x1)))))) 60.02/16.09 1(0(2(1(4(x1))))) -> 3(1(4(2(0(1(x1)))))) 60.02/16.09 1(0(2(1(4(x1))))) -> 1(1(2(2(0(4(x1)))))) 60.02/16.09 1(0(2(1(4(x1))))) -> 1(2(2(0(1(4(x1)))))) 60.02/16.09 1(0(3(1(4(x1))))) -> 1(2(0(3(1(4(x1)))))) 60.02/16.09 1(0(5(1(4(x1))))) -> 2(4(0(5(1(1(x1)))))) 60.02/16.09 1(1(5(1(4(x1))))) -> 1(1(2(5(4(1(x1)))))) 60.02/16.09 1(1(0(3(4(x1))))) -> 4(1(2(0(3(1(x1)))))) 60.02/16.09 1(1(0(3(4(x1))))) -> 2(0(4(1(3(1(x1)))))) 60.02/16.09 1(1(0(3(4(x1))))) -> 0(2(4(1(3(1(x1)))))) 60.02/16.09 1(1(0(3(4(x1))))) -> 1(4(2(0(1(3(x1)))))) 60.02/16.09 1(1(0(3(4(x1))))) -> 2(0(1(1(3(4(x1)))))) 60.02/16.09 1(0(1(3(4(x1))))) -> 1(3(1(2(4(0(x1)))))) 60.02/16.09 1(0(1(3(4(x1))))) -> 1(2(0(4(3(1(x1)))))) 60.02/16.09 1(0(2(3(4(x1))))) -> 1(2(2(0(4(3(x1)))))) 60.02/16.09 1(0(2(3(4(x1))))) -> 1(2(5(0(4(3(x1)))))) 60.02/16.09 1(0(2(3(4(x1))))) -> 1(3(1(2(0(4(x1)))))) 60.02/16.09 1(0(2(3(4(x1))))) -> 3(1(2(0(3(4(x1)))))) 60.02/16.09 1(1(2(3(4(x1))))) -> 2(4(2(1(3(1(x1)))))) 60.02/16.09 1(1(2(3(4(x1))))) -> 2(5(4(1(3(1(x1)))))) 60.02/16.09 1(1(2(3(4(x1))))) -> 2(1(4(3(1(3(x1)))))) 60.02/16.09 1(1(2(3(4(x1))))) -> 2(2(1(3(1(4(x1)))))) 60.02/16.09 1(1(2(3(4(x1))))) -> 2(1(3(3(1(4(x1)))))) 60.02/16.09 1(0(3(3(4(x1))))) -> 1(2(0(3(3(4(x1)))))) 60.02/16.09 1(0(4(3(4(x1))))) -> 1(2(4(0(4(3(x1)))))) 60.02/16.09 1(0(4(3(4(x1))))) -> 3(1(2(0(4(4(x1)))))) 60.02/16.09 1(0(5(3(4(x1))))) -> 4(1(3(2(5(0(x1)))))) 60.02/16.09 1(0(5(3(4(x1))))) -> 4(5(2(0(3(1(x1)))))) 60.02/16.09 1(0(5(3(4(x1))))) -> 5(2(4(0(3(1(x1)))))) 60.02/16.09 1(0(5(3(4(x1))))) -> 2(5(0(4(3(1(x1)))))) 60.02/16.09 1(0(5(3(4(x1))))) -> 5(2(4(0(1(3(x1)))))) 60.02/16.09 1(0(5(3(4(x1))))) -> 2(4(0(5(1(3(x1)))))) 60.02/16.09 1(0(5(3(4(x1))))) -> 5(1(2(0(4(3(x1)))))) 60.02/16.09 1(0(5(3(4(x1))))) -> 2(0(5(1(4(3(x1)))))) 60.02/16.09 1(0(5(3(4(x1))))) -> 2(4(0(1(5(3(x1)))))) 60.02/16.09 1(0(5(3(4(x1))))) -> 5(1(2(0(3(4(x1)))))) 60.02/16.09 1(0(5(3(4(x1))))) -> 2(0(4(3(1(5(x1)))))) 60.02/16.09 1(1(5(3(4(x1))))) -> 3(1(2(5(4(1(x1)))))) 60.02/16.09 1(1(5(3(4(x1))))) -> 2(4(5(1(1(3(x1)))))) 60.02/16.09 1(1(5(3(4(x1))))) -> 1(2(5(4(1(3(x1)))))) 60.02/16.09 1(1(5(3(4(x1))))) -> 5(3(1(3(1(4(x1)))))) 60.02/16.09 1(1(5(3(4(x1))))) -> 3(1(2(5(1(4(x1)))))) 60.02/16.09 1(1(5(3(4(x1))))) -> 1(2(5(1(3(4(x1)))))) 60.02/16.09 1(0(1(4(4(x1))))) -> 1(2(0(1(4(4(x1)))))) 60.02/16.09 1(0(3(4(4(x1))))) -> 3(1(2(4(4(0(x1)))))) 60.02/16.09 1(0(3(4(4(x1))))) -> 4(3(1(2(0(4(x1)))))) 60.02/16.09 1(0(3(4(4(x1))))) -> 1(2(0(4(3(4(x1)))))) 60.02/16.09 1(0(3(4(4(x1))))) -> 1(2(0(3(4(4(x1)))))) 60.02/16.09 1(0(1(5(4(x1))))) -> 1(4(3(1(5(0(x1)))))) 60.02/16.09 1(0(1(5(4(x1))))) -> 1(3(1(4(5(0(x1)))))) 60.02/16.09 1(0(1(5(4(x1))))) -> 1(2(5(4(0(1(x1)))))) 60.02/16.09 1(0(1(5(4(x1))))) -> 1(1(2(5(0(4(x1)))))) 60.02/16.09 1(0(1(5(4(x1))))) -> 1(2(0(1(5(4(x1)))))) 60.02/16.09 1(0(1(5(4(x1))))) -> 1(4(2(0(1(5(x1)))))) 60.02/16.09 1(0(1(5(4(x1))))) -> 1(2(0(1(4(5(x1)))))) 60.02/16.09 1(1(1(5(4(x1))))) -> 1(1(1(2(5(4(x1)))))) 60.02/16.09 1(0(3(5(4(x1))))) -> 5(4(3(1(2(0(x1)))))) 60.02/16.09 1(0(3(5(4(x1))))) -> 4(3(1(2(5(0(x1)))))) 60.02/16.09 1(0(3(5(4(x1))))) -> 1(3(4(2(5(0(x1)))))) 60.02/16.09 1(0(3(5(4(x1))))) -> 3(1(2(4(5(0(x1)))))) 60.02/16.09 1(0(3(5(4(x1))))) -> 4(3(1(5(0(1(x1)))))) 60.02/16.09 1(0(3(5(4(x1))))) -> 4(3(3(0(5(1(x1)))))) 60.02/16.09 1(0(3(5(4(x1))))) -> 3(0(5(4(1(2(x1)))))) 60.02/16.09 1(0(3(5(4(x1))))) -> 0(5(3(1(4(2(x1)))))) 60.02/16.09 1(0(3(5(4(x1))))) -> 1(2(5(4(0(3(x1)))))) 60.02/16.09 1(0(3(5(4(x1))))) -> 2(5(1(3(0(4(x1)))))) 60.02/16.09 1(0(3(5(4(x1))))) -> 1(5(3(3(0(4(x1)))))) 60.02/16.09 1(0(3(5(4(x1))))) -> 3(1(4(5(0(4(x1)))))) 60.02/16.09 1(0(3(5(4(x1))))) -> 3(0(5(3(1(4(x1)))))) 60.02/16.09 1(0(3(5(4(x1))))) -> 0(5(5(3(1(4(x1)))))) 60.02/16.09 1(0(3(5(4(x1))))) -> 1(3(0(5(2(4(x1)))))) 60.02/16.09 1(0(3(5(4(x1))))) -> 1(3(0(2(5(4(x1)))))) 60.02/16.09 1(0(3(5(4(x1))))) -> 1(4(1(3(0(5(x1)))))) 60.02/16.09 1(0(3(5(4(x1))))) -> 1(4(4(3(0(5(x1)))))) 60.02/16.09 1(0(3(5(4(x1))))) -> 4(3(0(3(1(5(x1)))))) 60.02/16.09 1(0(3(5(4(x1))))) -> 0(4(3(1(2(5(x1)))))) 60.02/16.09 1(0(3(5(4(x1))))) -> 0(3(1(4(2(5(x1)))))) 60.02/16.09 1(0(3(5(4(x1))))) -> 1(2(4(0(3(5(x1)))))) 60.02/16.09 1(0(3(5(4(x1))))) -> 1(0(3(1(4(5(x1)))))) 60.02/16.09 1(0(3(5(4(x1))))) -> 0(2(3(1(4(5(x1)))))) 60.02/16.09 1(0(3(5(4(x1))))) -> 1(2(0(3(4(5(x1)))))) 60.02/16.09 1(1(3(5(4(x1))))) -> 5(1(3(1(4(2(x1)))))) 60.02/16.09 1(1(3(5(4(x1))))) -> 1(3(1(2(5(4(x1)))))) 60.02/16.09 1(1(3(5(4(x1))))) -> 2(1(4(3(1(5(x1)))))) 60.02/16.09 1(1(3(5(4(x1))))) -> 3(1(4(1(2(5(x1)))))) 60.02/16.09 1(1(3(5(4(x1))))) -> 1(3(1(2(4(5(x1)))))) 60.02/16.09 1(1(5(5(4(x1))))) -> 4(1(1(2(5(5(x1)))))) 60.02/16.09 1(1(5(5(4(x1))))) -> 1(1(4(2(5(5(x1)))))) 60.02/16.09 60.02/16.09 Q is empty. 60.02/16.09 60.02/16.09 ---------------------------------------- 60.02/16.09 60.02/16.09 (3) DependencyPairsProof (EQUIVALENT) 60.02/16.09 Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. 60.02/16.09 ---------------------------------------- 60.02/16.09 60.02/16.09 (4) 60.02/16.09 Obligation: 60.02/16.09 Q DP problem: 60.02/16.09 The TRS P consists of the following rules: 60.02/16.09 60.02/16.09 1^1(0(1(0(x1)))) -> 1^1(3(1(2(0(0(x1)))))) 60.02/16.09 1^1(0(1(0(x1)))) -> 1^1(2(0(0(x1)))) 60.02/16.09 1^1(0(1(0(x1)))) -> 1^1(0(2(0(1(2(x1)))))) 60.02/16.09 1^1(0(1(0(x1)))) -> 1^1(2(x1)) 60.02/16.09 1^1(0(1(0(x1)))) -> 1^1(3(1(2(x1)))) 60.02/16.09 1^1(0(1(4(x1)))) -> 1^1(2(4(0(1(x1))))) 60.02/16.09 1^1(0(1(4(x1)))) -> 1^1(x1) 60.02/16.09 1^1(0(1(4(x1)))) -> 1^1(2(0(1(4(x1))))) 60.02/16.09 1^1(0(1(4(x1)))) -> 1^1(4(3(1(2(0(x1)))))) 60.02/16.09 1^1(0(1(4(x1)))) -> 1^1(2(0(x1))) 60.02/16.09 1^1(0(1(4(x1)))) -> 1^1(3(1(2(4(0(x1)))))) 60.02/16.09 1^1(0(1(4(x1)))) -> 1^1(2(4(0(x1)))) 60.02/16.09 1^1(0(1(4(x1)))) -> 1^1(4(2(0(1(x1))))) 60.02/16.09 1^1(0(1(4(x1)))) -> 1^1(2(2(4(0(1(x1)))))) 60.02/16.09 1^1(0(1(4(x1)))) -> 1^1(2(5(4(0(1(x1)))))) 60.02/16.09 1^1(0(1(4(x1)))) -> 1^1(3(1(2(0(4(x1)))))) 60.02/16.09 1^1(0(1(4(x1)))) -> 1^1(2(0(4(x1)))) 60.02/16.09 1^1(0(1(4(x1)))) -> 1^1(2(0(3(1(4(x1)))))) 60.02/16.09 1^1(1(1(4(x1)))) -> 1^1(3(1(3(1(4(x1)))))) 60.02/16.09 1^1(1(1(4(x1)))) -> 1^1(3(1(4(x1)))) 60.02/16.09 1^1(0(3(4(x1)))) -> 1^1(2(0(x1))) 60.02/16.09 1^1(0(3(4(x1)))) -> 1^1(4(2(0(x1)))) 60.02/16.09 1^1(0(3(4(x1)))) -> 1^1(2(4(0(x1)))) 60.02/16.09 1^1(0(3(4(x1)))) -> 1^1(2(4(0(3(x1))))) 60.02/16.09 1^1(0(3(4(x1)))) -> 1^1(2(0(4(3(x1))))) 60.02/16.09 1^1(0(3(4(x1)))) -> 1^1(2(0(4(x1)))) 60.02/16.09 1^1(0(3(4(x1)))) -> 1^1(2(0(3(4(x1))))) 60.02/16.09 1^1(0(3(4(x1)))) -> 1^1(2(2(4(0(x1))))) 60.02/16.09 1^1(0(3(4(x1)))) -> 1^1(2(5(4(0(x1))))) 60.02/16.09 1^1(0(3(4(x1)))) -> 1^1(2(0(1(x1)))) 60.02/16.09 1^1(0(3(4(x1)))) -> 1^1(x1) 60.02/16.09 1^1(0(3(4(x1)))) -> 1^1(4(2(0(1(x1))))) 60.02/16.09 1^1(0(3(4(x1)))) -> 1^1(2(4(0(1(x1))))) 60.02/16.09 1^1(0(3(4(x1)))) -> 1^1(2(4(0(3(1(x1)))))) 60.02/16.09 1^1(0(3(4(x1)))) -> 1^1(2(5(4(0(3(x1)))))) 60.02/16.09 1^1(0(3(4(x1)))) -> 1^1(2(4(0(1(3(x1)))))) 60.02/16.09 1^1(0(3(4(x1)))) -> 1^1(3(x1)) 60.02/16.09 1^1(0(3(4(x1)))) -> 1^1(2(0(4(3(3(x1)))))) 60.02/16.09 1^1(0(3(4(x1)))) -> 1^1(2(2(0(4(3(x1)))))) 60.02/16.09 1^1(0(3(4(x1)))) -> 1^1(2(5(0(4(3(x1)))))) 60.02/16.09 1^1(0(3(4(x1)))) -> 1^1(2(0(1(4(3(x1)))))) 60.02/16.09 1^1(0(3(4(x1)))) -> 1^1(4(3(x1))) 60.02/16.09 1^1(0(3(4(x1)))) -> 1^1(2(0(3(4(3(x1)))))) 60.02/16.09 1^1(0(3(4(x1)))) -> 1^1(2(5(0(3(4(x1)))))) 60.02/16.09 1^1(0(3(4(x1)))) -> 1^1(2(0(1(3(4(x1)))))) 60.02/16.09 1^1(0(3(4(x1)))) -> 1^1(3(4(x1))) 60.02/16.09 1^1(0(3(4(x1)))) -> 1^1(2(0(3(3(4(x1)))))) 60.02/16.09 1^1(1(5(4(x1)))) -> 1^1(1(2(5(4(x1))))) 60.02/16.09 1^1(1(5(4(x1)))) -> 1^1(2(5(4(x1)))) 60.02/16.09 1^1(1(5(4(x1)))) -> 1^1(1(2(5(2(4(x1)))))) 60.02/16.09 1^1(1(5(4(x1)))) -> 1^1(2(5(2(4(x1))))) 60.02/16.09 1^1(1(5(4(x1)))) -> 1^1(3(1(2(5(4(x1)))))) 60.02/16.09 1^1(1(5(4(x1)))) -> 1^1(1(2(2(5(4(x1)))))) 60.02/16.09 1^1(1(5(4(x1)))) -> 1^1(2(2(5(4(x1))))) 60.02/16.09 1^1(1(5(4(x1)))) -> 1^1(1(2(5(5(4(x1)))))) 60.02/16.09 1^1(1(5(4(x1)))) -> 1^1(2(5(5(4(x1))))) 60.02/16.09 1^1(0(1(0(0(x1))))) -> 1^1(2(0(1(0(0(x1)))))) 60.02/16.09 1^1(1(3(0(0(x1))))) -> 1^1(3(1(2(x1)))) 60.02/16.09 1^1(1(3(0(0(x1))))) -> 1^1(2(x1)) 60.02/16.09 1^1(1(5(0(0(x1))))) -> 1^1(1(2(0(0(5(x1)))))) 60.02/16.09 1^1(1(5(0(0(x1))))) -> 1^1(2(0(0(5(x1))))) 60.02/16.09 1^1(0(1(4(0(x1))))) -> 1^1(0(4(0(1(2(x1)))))) 60.02/16.09 1^1(0(1(4(0(x1))))) -> 1^1(2(x1)) 60.02/16.09 1^1(0(3(4(0(x1))))) -> 1^1(2(0(0(x1)))) 60.02/16.09 1^1(0(3(4(0(x1))))) -> 1^1(2(0(3(4(0(x1)))))) 60.02/16.09 1^1(0(3(4(0(x1))))) -> 1^1(3(2(x1))) 60.02/16.09 1^1(1(3(4(0(x1))))) -> 1^1(4(1(2(x1)))) 60.02/16.09 1^1(1(3(4(0(x1))))) -> 1^1(2(x1)) 60.02/16.09 1^1(1(3(4(0(x1))))) -> 1^1(1(3(0(2(4(x1)))))) 60.02/16.09 1^1(1(3(4(0(x1))))) -> 1^1(3(0(2(4(x1))))) 60.02/16.09 1^1(1(5(4(0(x1))))) -> 1^1(2(5(1(0(4(x1)))))) 60.02/16.09 1^1(1(5(4(0(x1))))) -> 1^1(0(4(x1))) 60.02/16.09 1^1(1(5(4(0(x1))))) -> 1^1(0(4(1(2(5(x1)))))) 60.02/16.09 1^1(1(5(4(0(x1))))) -> 1^1(2(5(x1))) 60.02/16.09 1^1(0(3(0(4(x1))))) -> 1^1(2(4(0(0(x1))))) 60.02/16.09 1^1(0(3(0(4(x1))))) -> 1^1(0(4(0(2(x1))))) 60.02/16.09 1^1(0(3(0(4(x1))))) -> 1^1(3(0(4(0(2(x1)))))) 60.02/16.09 1^1(1(0(1(4(x1))))) -> 1^1(1(2(4(0(1(x1)))))) 60.02/16.09 1^1(1(0(1(4(x1))))) -> 1^1(2(4(0(1(x1))))) 60.02/16.09 1^1(1(0(1(4(x1))))) -> 1^1(x1) 60.02/16.09 1^1(0(1(1(4(x1))))) -> 1^1(1(2(0(1(4(x1)))))) 60.02/16.09 1^1(0(1(1(4(x1))))) -> 1^1(2(0(1(4(x1))))) 60.02/16.09 1^1(0(2(1(4(x1))))) -> 1^1(3(1(2(4(0(x1)))))) 60.02/16.09 1^1(0(2(1(4(x1))))) -> 1^1(2(4(0(x1)))) 60.02/16.09 1^1(0(2(1(4(x1))))) -> 1^1(4(2(0(1(x1))))) 60.02/16.09 1^1(0(2(1(4(x1))))) -> 1^1(x1) 60.02/16.09 1^1(0(2(1(4(x1))))) -> 1^1(1(2(2(0(4(x1)))))) 60.02/16.09 1^1(0(2(1(4(x1))))) -> 1^1(2(2(0(4(x1))))) 60.02/16.09 1^1(0(2(1(4(x1))))) -> 1^1(2(2(0(1(4(x1)))))) 60.02/16.09 1^1(0(3(1(4(x1))))) -> 1^1(2(0(3(1(4(x1)))))) 60.02/16.09 1^1(0(5(1(4(x1))))) -> 1^1(1(x1)) 60.02/16.09 1^1(0(5(1(4(x1))))) -> 1^1(x1) 60.02/16.09 1^1(1(5(1(4(x1))))) -> 1^1(1(2(5(4(1(x1)))))) 60.02/16.09 1^1(1(5(1(4(x1))))) -> 1^1(2(5(4(1(x1))))) 60.02/16.09 1^1(1(5(1(4(x1))))) -> 1^1(x1) 60.02/16.09 1^1(1(0(3(4(x1))))) -> 1^1(2(0(3(1(x1))))) 60.02/16.09 1^1(1(0(3(4(x1))))) -> 1^1(x1) 60.02/16.09 1^1(1(0(3(4(x1))))) -> 1^1(3(1(x1))) 60.02/16.09 1^1(1(0(3(4(x1))))) -> 1^1(4(2(0(1(3(x1)))))) 60.02/16.09 1^1(1(0(3(4(x1))))) -> 1^1(3(x1)) 60.02/16.09 1^1(1(0(3(4(x1))))) -> 1^1(1(3(4(x1)))) 60.02/16.09 1^1(1(0(3(4(x1))))) -> 1^1(3(4(x1))) 60.02/16.09 1^1(0(1(3(4(x1))))) -> 1^1(3(1(2(4(0(x1)))))) 60.02/16.09 1^1(0(1(3(4(x1))))) -> 1^1(2(4(0(x1)))) 60.02/16.09 1^1(0(1(3(4(x1))))) -> 1^1(2(0(4(3(1(x1)))))) 60.02/16.09 1^1(0(1(3(4(x1))))) -> 1^1(x1) 60.02/16.09 1^1(0(2(3(4(x1))))) -> 1^1(2(2(0(4(3(x1)))))) 60.02/16.09 1^1(0(2(3(4(x1))))) -> 1^1(2(5(0(4(3(x1)))))) 60.02/16.09 1^1(0(2(3(4(x1))))) -> 1^1(3(1(2(0(4(x1)))))) 60.02/16.09 1^1(0(2(3(4(x1))))) -> 1^1(2(0(4(x1)))) 60.02/16.09 1^1(0(2(3(4(x1))))) -> 1^1(2(0(3(4(x1))))) 60.02/16.09 1^1(1(2(3(4(x1))))) -> 1^1(3(1(x1))) 60.02/16.09 1^1(1(2(3(4(x1))))) -> 1^1(x1) 60.02/16.09 1^1(1(2(3(4(x1))))) -> 1^1(4(3(1(3(x1))))) 60.02/16.09 1^1(1(2(3(4(x1))))) -> 1^1(3(x1)) 60.02/16.09 1^1(1(2(3(4(x1))))) -> 1^1(3(1(4(x1)))) 60.02/16.09 1^1(1(2(3(4(x1))))) -> 1^1(4(x1)) 60.02/16.09 1^1(1(2(3(4(x1))))) -> 1^1(3(3(1(4(x1))))) 60.02/16.09 1^1(0(3(3(4(x1))))) -> 1^1(2(0(3(3(4(x1)))))) 60.02/16.09 1^1(0(4(3(4(x1))))) -> 1^1(2(4(0(4(3(x1)))))) 60.02/16.09 1^1(0(4(3(4(x1))))) -> 1^1(2(0(4(4(x1))))) 60.02/16.09 1^1(0(5(3(4(x1))))) -> 1^1(3(2(5(0(x1))))) 60.02/16.09 1^1(0(5(3(4(x1))))) -> 1^1(x1) 60.02/16.09 1^1(0(5(3(4(x1))))) -> 1^1(3(x1)) 60.02/16.09 1^1(0(5(3(4(x1))))) -> 1^1(2(0(4(3(x1))))) 60.02/16.09 1^1(0(5(3(4(x1))))) -> 1^1(4(3(x1))) 60.02/16.09 1^1(0(5(3(4(x1))))) -> 1^1(5(3(x1))) 60.02/16.09 1^1(0(5(3(4(x1))))) -> 1^1(2(0(3(4(x1))))) 60.02/16.09 1^1(0(5(3(4(x1))))) -> 1^1(5(x1)) 60.02/16.09 1^1(1(5(3(4(x1))))) -> 1^1(2(5(4(1(x1))))) 60.02/16.09 1^1(1(5(3(4(x1))))) -> 1^1(x1) 60.02/16.09 1^1(1(5(3(4(x1))))) -> 1^1(1(3(x1))) 60.02/16.09 1^1(1(5(3(4(x1))))) -> 1^1(3(x1)) 60.02/16.09 1^1(1(5(3(4(x1))))) -> 1^1(2(5(4(1(3(x1)))))) 60.02/16.09 1^1(1(5(3(4(x1))))) -> 1^1(3(1(4(x1)))) 60.02/16.09 1^1(1(5(3(4(x1))))) -> 1^1(4(x1)) 60.02/16.09 1^1(1(5(3(4(x1))))) -> 1^1(2(5(1(4(x1))))) 60.02/16.09 1^1(1(5(3(4(x1))))) -> 1^1(2(5(1(3(4(x1)))))) 60.02/16.09 1^1(1(5(3(4(x1))))) -> 1^1(3(4(x1))) 60.02/16.09 1^1(0(1(4(4(x1))))) -> 1^1(2(0(1(4(4(x1)))))) 60.02/16.09 1^1(0(3(4(4(x1))))) -> 1^1(2(4(4(0(x1))))) 60.02/16.09 1^1(0(3(4(4(x1))))) -> 1^1(2(0(4(x1)))) 60.02/16.09 1^1(0(3(4(4(x1))))) -> 1^1(2(0(4(3(4(x1)))))) 60.02/16.09 1^1(0(3(4(4(x1))))) -> 1^1(2(0(3(4(4(x1)))))) 60.02/16.09 1^1(0(1(5(4(x1))))) -> 1^1(4(3(1(5(0(x1)))))) 60.02/16.09 1^1(0(1(5(4(x1))))) -> 1^1(5(0(x1))) 60.02/16.09 1^1(0(1(5(4(x1))))) -> 1^1(3(1(4(5(0(x1)))))) 60.02/16.09 1^1(0(1(5(4(x1))))) -> 1^1(4(5(0(x1)))) 60.02/16.09 1^1(0(1(5(4(x1))))) -> 1^1(2(5(4(0(1(x1)))))) 60.02/16.09 1^1(0(1(5(4(x1))))) -> 1^1(x1) 60.02/16.09 1^1(0(1(5(4(x1))))) -> 1^1(1(2(5(0(4(x1)))))) 60.02/16.09 1^1(0(1(5(4(x1))))) -> 1^1(2(5(0(4(x1))))) 60.02/16.09 1^1(0(1(5(4(x1))))) -> 1^1(2(0(1(5(4(x1)))))) 60.02/16.09 1^1(0(1(5(4(x1))))) -> 1^1(4(2(0(1(5(x1)))))) 60.02/16.09 1^1(0(1(5(4(x1))))) -> 1^1(5(x1)) 60.02/16.09 1^1(0(1(5(4(x1))))) -> 1^1(2(0(1(4(5(x1)))))) 60.02/16.09 1^1(0(1(5(4(x1))))) -> 1^1(4(5(x1))) 60.02/16.09 1^1(1(1(5(4(x1))))) -> 1^1(1(1(2(5(4(x1)))))) 60.02/16.09 1^1(1(1(5(4(x1))))) -> 1^1(1(2(5(4(x1))))) 60.02/16.09 1^1(1(1(5(4(x1))))) -> 1^1(2(5(4(x1)))) 60.02/16.09 1^1(0(3(5(4(x1))))) -> 1^1(2(0(x1))) 60.02/16.09 1^1(0(3(5(4(x1))))) -> 1^1(2(5(0(x1)))) 60.02/16.09 1^1(0(3(5(4(x1))))) -> 1^1(3(4(2(5(0(x1)))))) 60.02/16.09 1^1(0(3(5(4(x1))))) -> 1^1(2(4(5(0(x1))))) 60.02/16.09 1^1(0(3(5(4(x1))))) -> 1^1(5(0(1(x1)))) 60.02/16.09 1^1(0(3(5(4(x1))))) -> 1^1(x1) 60.02/16.09 1^1(0(3(5(4(x1))))) -> 1^1(2(x1)) 60.02/16.09 1^1(0(3(5(4(x1))))) -> 1^1(4(2(x1))) 60.02/16.09 1^1(0(3(5(4(x1))))) -> 1^1(2(5(4(0(3(x1)))))) 60.02/16.09 1^1(0(3(5(4(x1))))) -> 1^1(3(0(4(x1)))) 60.02/16.09 1^1(0(3(5(4(x1))))) -> 1^1(5(3(3(0(4(x1)))))) 60.02/16.09 1^1(0(3(5(4(x1))))) -> 1^1(4(5(0(4(x1))))) 60.02/16.09 1^1(0(3(5(4(x1))))) -> 1^1(4(x1)) 60.02/16.09 1^1(0(3(5(4(x1))))) -> 1^1(3(0(5(2(4(x1)))))) 60.02/16.09 1^1(0(3(5(4(x1))))) -> 1^1(3(0(2(5(4(x1)))))) 60.02/16.09 1^1(0(3(5(4(x1))))) -> 1^1(4(1(3(0(5(x1)))))) 60.02/16.09 1^1(0(3(5(4(x1))))) -> 1^1(3(0(5(x1)))) 60.02/16.09 1^1(0(3(5(4(x1))))) -> 1^1(4(4(3(0(5(x1)))))) 60.02/16.09 1^1(0(3(5(4(x1))))) -> 1^1(5(x1)) 60.02/16.09 1^1(0(3(5(4(x1))))) -> 1^1(2(5(x1))) 60.02/16.09 1^1(0(3(5(4(x1))))) -> 1^1(4(2(5(x1)))) 60.02/16.09 1^1(0(3(5(4(x1))))) -> 1^1(2(4(0(3(5(x1)))))) 60.02/16.09 1^1(0(3(5(4(x1))))) -> 1^1(0(3(1(4(5(x1)))))) 60.02/16.09 1^1(0(3(5(4(x1))))) -> 1^1(4(5(x1))) 60.02/16.09 1^1(0(3(5(4(x1))))) -> 1^1(2(0(3(4(5(x1)))))) 60.02/16.09 1^1(1(3(5(4(x1))))) -> 1^1(3(1(4(2(x1))))) 60.02/16.09 1^1(1(3(5(4(x1))))) -> 1^1(4(2(x1))) 60.02/16.09 1^1(1(3(5(4(x1))))) -> 1^1(3(1(2(5(4(x1)))))) 60.02/16.09 1^1(1(3(5(4(x1))))) -> 1^1(2(5(4(x1)))) 60.02/16.09 1^1(1(3(5(4(x1))))) -> 1^1(4(3(1(5(x1))))) 60.02/16.09 1^1(1(3(5(4(x1))))) -> 1^1(5(x1)) 60.02/16.09 1^1(1(3(5(4(x1))))) -> 1^1(4(1(2(5(x1))))) 60.02/16.09 1^1(1(3(5(4(x1))))) -> 1^1(2(5(x1))) 60.02/16.09 1^1(1(3(5(4(x1))))) -> 1^1(3(1(2(4(5(x1)))))) 60.02/16.09 1^1(1(3(5(4(x1))))) -> 1^1(2(4(5(x1)))) 60.02/16.09 1^1(1(5(5(4(x1))))) -> 1^1(1(2(5(5(x1))))) 60.02/16.09 1^1(1(5(5(4(x1))))) -> 1^1(2(5(5(x1)))) 60.02/16.09 1^1(1(5(5(4(x1))))) -> 1^1(1(4(2(5(5(x1)))))) 60.02/16.09 1^1(1(5(5(4(x1))))) -> 1^1(4(2(5(5(x1))))) 60.02/16.09 60.02/16.09 The TRS R consists of the following rules: 60.02/16.09 60.02/16.09 1(0(1(0(x1)))) -> 1(3(1(2(0(0(x1)))))) 60.02/16.09 1(0(1(0(x1)))) -> 1(0(2(0(1(2(x1)))))) 60.02/16.09 1(0(1(0(x1)))) -> 0(0(1(3(1(2(x1)))))) 60.02/16.09 1(0(1(4(x1)))) -> 1(2(4(0(1(x1))))) 60.02/16.09 1(0(1(4(x1)))) -> 1(2(0(1(4(x1))))) 60.02/16.09 1(0(1(4(x1)))) -> 1(4(3(1(2(0(x1)))))) 60.02/16.09 1(0(1(4(x1)))) -> 1(3(1(2(4(0(x1)))))) 60.02/16.09 1(0(1(4(x1)))) -> 3(1(4(2(0(1(x1)))))) 60.02/16.09 1(0(1(4(x1)))) -> 1(2(2(4(0(1(x1)))))) 60.02/16.09 1(0(1(4(x1)))) -> 1(2(5(4(0(1(x1)))))) 60.02/16.09 1(0(1(4(x1)))) -> 1(3(1(2(0(4(x1)))))) 60.02/16.09 1(0(1(4(x1)))) -> 3(1(2(0(1(4(x1)))))) 60.02/16.09 1(0(1(4(x1)))) -> 1(2(0(3(1(4(x1)))))) 60.02/16.09 1(1(1(4(x1)))) -> 1(3(1(3(1(4(x1)))))) 60.02/16.09 1(0(3(4(x1)))) -> 4(3(1(2(0(x1))))) 60.02/16.09 1(0(3(4(x1)))) -> 3(1(4(2(0(x1))))) 60.02/16.09 1(0(3(4(x1)))) -> 3(1(2(4(0(x1))))) 60.02/16.09 1(0(3(4(x1)))) -> 1(2(4(0(3(x1))))) 60.02/16.09 1(0(3(4(x1)))) -> 1(2(0(4(3(x1))))) 60.02/16.09 1(0(3(4(x1)))) -> 3(1(2(0(4(x1))))) 60.02/16.09 1(0(3(4(x1)))) -> 1(2(0(3(4(x1))))) 60.02/16.09 1(0(3(4(x1)))) -> 4(3(3(1(2(0(x1)))))) 60.02/16.09 1(0(3(4(x1)))) -> 3(4(3(1(2(0(x1)))))) 60.02/16.09 1(0(3(4(x1)))) -> 3(3(1(4(2(0(x1)))))) 60.02/16.09 1(0(3(4(x1)))) -> 3(1(2(2(4(0(x1)))))) 60.02/16.09 1(0(3(4(x1)))) -> 3(1(2(5(4(0(x1)))))) 60.02/16.09 1(0(3(4(x1)))) -> 4(3(1(2(0(1(x1)))))) 60.02/16.09 1(0(3(4(x1)))) -> 3(1(4(2(0(1(x1)))))) 60.02/16.09 1(0(3(4(x1)))) -> 3(1(2(4(0(1(x1)))))) 60.02/16.09 1(0(3(4(x1)))) -> 1(2(4(0(3(1(x1)))))) 60.02/16.09 1(0(3(4(x1)))) -> 1(2(5(4(0(3(x1)))))) 60.02/16.09 1(0(3(4(x1)))) -> 1(2(4(0(1(3(x1)))))) 60.02/16.09 1(0(3(4(x1)))) -> 1(2(0(4(3(3(x1)))))) 60.02/16.09 1(0(3(4(x1)))) -> 3(1(2(0(4(3(x1)))))) 60.02/16.09 1(0(3(4(x1)))) -> 1(2(2(0(4(3(x1)))))) 60.02/16.09 1(0(3(4(x1)))) -> 1(2(5(0(4(3(x1)))))) 60.02/16.09 1(0(3(4(x1)))) -> 1(2(0(1(4(3(x1)))))) 60.02/16.09 1(0(3(4(x1)))) -> 1(2(0(3(4(3(x1)))))) 60.02/16.09 1(0(3(4(x1)))) -> 3(1(2(0(3(4(x1)))))) 60.02/16.09 1(0(3(4(x1)))) -> 1(2(5(0(3(4(x1)))))) 60.02/16.09 1(0(3(4(x1)))) -> 1(2(0(1(3(4(x1)))))) 60.02/16.09 1(0(3(4(x1)))) -> 1(2(0(3(3(4(x1)))))) 60.02/16.09 1(1(5(4(x1)))) -> 1(1(2(5(4(x1))))) 60.02/16.09 1(1(5(4(x1)))) -> 1(1(2(5(2(4(x1)))))) 60.02/16.09 1(1(5(4(x1)))) -> 1(3(1(2(5(4(x1)))))) 60.02/16.09 1(1(5(4(x1)))) -> 1(1(2(2(5(4(x1)))))) 60.02/16.09 1(1(5(4(x1)))) -> 1(1(2(5(5(4(x1)))))) 60.02/16.09 1(0(1(0(0(x1))))) -> 1(2(0(1(0(0(x1)))))) 60.02/16.09 1(1(3(0(0(x1))))) -> 0(0(1(3(1(2(x1)))))) 60.02/16.09 1(1(5(0(0(x1))))) -> 1(1(2(0(0(5(x1)))))) 60.02/16.09 1(0(1(4(0(x1))))) -> 1(0(4(0(1(2(x1)))))) 60.02/16.09 1(0(3(4(0(x1))))) -> 4(3(1(2(0(0(x1)))))) 60.02/16.09 1(0(3(4(0(x1))))) -> 1(2(0(3(4(0(x1)))))) 60.02/16.09 1(0(3(4(0(x1))))) -> 0(4(0(1(3(2(x1)))))) 60.02/16.09 1(1(3(4(0(x1))))) -> 0(3(1(4(1(2(x1)))))) 60.02/16.09 1(1(3(4(0(x1))))) -> 1(1(3(0(2(4(x1)))))) 60.02/16.09 1(1(5(4(0(x1))))) -> 1(2(5(1(0(4(x1)))))) 60.02/16.09 1(1(5(4(0(x1))))) -> 1(0(4(1(2(5(x1)))))) 60.02/16.10 1(0(3(0(4(x1))))) -> 3(1(2(4(0(0(x1)))))) 60.02/16.10 1(0(3(0(4(x1))))) -> 3(1(0(4(0(2(x1)))))) 60.02/16.10 1(0(3(0(4(x1))))) -> 1(3(0(4(0(2(x1)))))) 60.02/16.10 1(1(0(1(4(x1))))) -> 1(1(2(4(0(1(x1)))))) 60.02/16.10 1(0(1(1(4(x1))))) -> 1(1(2(0(1(4(x1)))))) 60.02/16.10 1(0(2(1(4(x1))))) -> 1(3(1(2(4(0(x1)))))) 60.02/16.10 1(0(2(1(4(x1))))) -> 3(1(4(2(0(1(x1)))))) 60.02/16.10 1(0(2(1(4(x1))))) -> 1(1(2(2(0(4(x1)))))) 60.02/16.10 1(0(2(1(4(x1))))) -> 1(2(2(0(1(4(x1)))))) 60.02/16.10 1(0(3(1(4(x1))))) -> 1(2(0(3(1(4(x1)))))) 60.02/16.10 1(0(5(1(4(x1))))) -> 2(4(0(5(1(1(x1)))))) 60.02/16.10 1(1(5(1(4(x1))))) -> 1(1(2(5(4(1(x1)))))) 60.02/16.10 1(1(0(3(4(x1))))) -> 4(1(2(0(3(1(x1)))))) 60.02/16.10 1(1(0(3(4(x1))))) -> 2(0(4(1(3(1(x1)))))) 60.02/16.10 1(1(0(3(4(x1))))) -> 0(2(4(1(3(1(x1)))))) 60.02/16.10 1(1(0(3(4(x1))))) -> 1(4(2(0(1(3(x1)))))) 60.02/16.10 1(1(0(3(4(x1))))) -> 2(0(1(1(3(4(x1)))))) 60.02/16.10 1(0(1(3(4(x1))))) -> 1(3(1(2(4(0(x1)))))) 60.02/16.10 1(0(1(3(4(x1))))) -> 1(2(0(4(3(1(x1)))))) 60.02/16.10 1(0(2(3(4(x1))))) -> 1(2(2(0(4(3(x1)))))) 60.02/16.10 1(0(2(3(4(x1))))) -> 1(2(5(0(4(3(x1)))))) 60.02/16.10 1(0(2(3(4(x1))))) -> 1(3(1(2(0(4(x1)))))) 60.02/16.10 1(0(2(3(4(x1))))) -> 3(1(2(0(3(4(x1)))))) 60.02/16.10 1(1(2(3(4(x1))))) -> 2(4(2(1(3(1(x1)))))) 60.02/16.10 1(1(2(3(4(x1))))) -> 2(5(4(1(3(1(x1)))))) 60.02/16.10 1(1(2(3(4(x1))))) -> 2(1(4(3(1(3(x1)))))) 60.02/16.10 1(1(2(3(4(x1))))) -> 2(2(1(3(1(4(x1)))))) 60.02/16.10 1(1(2(3(4(x1))))) -> 2(1(3(3(1(4(x1)))))) 60.02/16.10 1(0(3(3(4(x1))))) -> 1(2(0(3(3(4(x1)))))) 60.02/16.10 1(0(4(3(4(x1))))) -> 1(2(4(0(4(3(x1)))))) 60.02/16.10 1(0(4(3(4(x1))))) -> 3(1(2(0(4(4(x1)))))) 60.02/16.10 1(0(5(3(4(x1))))) -> 4(1(3(2(5(0(x1)))))) 60.02/16.10 1(0(5(3(4(x1))))) -> 4(5(2(0(3(1(x1)))))) 60.02/16.10 1(0(5(3(4(x1))))) -> 5(2(4(0(3(1(x1)))))) 60.02/16.10 1(0(5(3(4(x1))))) -> 2(5(0(4(3(1(x1)))))) 60.02/16.10 1(0(5(3(4(x1))))) -> 5(2(4(0(1(3(x1)))))) 60.02/16.10 1(0(5(3(4(x1))))) -> 2(4(0(5(1(3(x1)))))) 60.02/16.10 1(0(5(3(4(x1))))) -> 5(1(2(0(4(3(x1)))))) 60.02/16.10 1(0(5(3(4(x1))))) -> 2(0(5(1(4(3(x1)))))) 60.02/16.10 1(0(5(3(4(x1))))) -> 2(4(0(1(5(3(x1)))))) 60.02/16.10 1(0(5(3(4(x1))))) -> 5(1(2(0(3(4(x1)))))) 60.02/16.10 1(0(5(3(4(x1))))) -> 2(0(4(3(1(5(x1)))))) 60.02/16.10 1(1(5(3(4(x1))))) -> 3(1(2(5(4(1(x1)))))) 60.02/16.10 1(1(5(3(4(x1))))) -> 2(4(5(1(1(3(x1)))))) 60.02/16.10 1(1(5(3(4(x1))))) -> 1(2(5(4(1(3(x1)))))) 60.02/16.10 1(1(5(3(4(x1))))) -> 5(3(1(3(1(4(x1)))))) 60.02/16.10 1(1(5(3(4(x1))))) -> 3(1(2(5(1(4(x1)))))) 60.02/16.10 1(1(5(3(4(x1))))) -> 1(2(5(1(3(4(x1)))))) 60.02/16.10 1(0(1(4(4(x1))))) -> 1(2(0(1(4(4(x1)))))) 60.02/16.10 1(0(3(4(4(x1))))) -> 3(1(2(4(4(0(x1)))))) 60.02/16.10 1(0(3(4(4(x1))))) -> 4(3(1(2(0(4(x1)))))) 60.02/16.10 1(0(3(4(4(x1))))) -> 1(2(0(4(3(4(x1)))))) 60.02/16.10 1(0(3(4(4(x1))))) -> 1(2(0(3(4(4(x1)))))) 60.02/16.10 1(0(1(5(4(x1))))) -> 1(4(3(1(5(0(x1)))))) 60.02/16.10 1(0(1(5(4(x1))))) -> 1(3(1(4(5(0(x1)))))) 60.02/16.10 1(0(1(5(4(x1))))) -> 1(2(5(4(0(1(x1)))))) 60.02/16.10 1(0(1(5(4(x1))))) -> 1(1(2(5(0(4(x1)))))) 60.02/16.10 1(0(1(5(4(x1))))) -> 1(2(0(1(5(4(x1)))))) 60.02/16.10 1(0(1(5(4(x1))))) -> 1(4(2(0(1(5(x1)))))) 60.02/16.10 1(0(1(5(4(x1))))) -> 1(2(0(1(4(5(x1)))))) 60.02/16.10 1(1(1(5(4(x1))))) -> 1(1(1(2(5(4(x1)))))) 60.02/16.10 1(0(3(5(4(x1))))) -> 5(4(3(1(2(0(x1)))))) 60.02/16.10 1(0(3(5(4(x1))))) -> 4(3(1(2(5(0(x1)))))) 60.02/16.10 1(0(3(5(4(x1))))) -> 1(3(4(2(5(0(x1)))))) 60.02/16.10 1(0(3(5(4(x1))))) -> 3(1(2(4(5(0(x1)))))) 60.02/16.10 1(0(3(5(4(x1))))) -> 4(3(1(5(0(1(x1)))))) 60.02/16.10 1(0(3(5(4(x1))))) -> 4(3(3(0(5(1(x1)))))) 60.02/16.10 1(0(3(5(4(x1))))) -> 3(0(5(4(1(2(x1)))))) 60.02/16.10 1(0(3(5(4(x1))))) -> 0(5(3(1(4(2(x1)))))) 60.02/16.10 1(0(3(5(4(x1))))) -> 1(2(5(4(0(3(x1)))))) 60.02/16.10 1(0(3(5(4(x1))))) -> 2(5(1(3(0(4(x1)))))) 60.02/16.10 1(0(3(5(4(x1))))) -> 1(5(3(3(0(4(x1)))))) 60.02/16.10 1(0(3(5(4(x1))))) -> 3(1(4(5(0(4(x1)))))) 60.02/16.10 1(0(3(5(4(x1))))) -> 3(0(5(3(1(4(x1)))))) 60.02/16.10 1(0(3(5(4(x1))))) -> 0(5(5(3(1(4(x1)))))) 60.02/16.10 1(0(3(5(4(x1))))) -> 1(3(0(5(2(4(x1)))))) 60.02/16.10 1(0(3(5(4(x1))))) -> 1(3(0(2(5(4(x1)))))) 60.02/16.10 1(0(3(5(4(x1))))) -> 1(4(1(3(0(5(x1)))))) 60.02/16.10 1(0(3(5(4(x1))))) -> 1(4(4(3(0(5(x1)))))) 60.02/16.10 1(0(3(5(4(x1))))) -> 4(3(0(3(1(5(x1)))))) 60.02/16.10 1(0(3(5(4(x1))))) -> 0(4(3(1(2(5(x1)))))) 60.02/16.10 1(0(3(5(4(x1))))) -> 0(3(1(4(2(5(x1)))))) 60.02/16.10 1(0(3(5(4(x1))))) -> 1(2(4(0(3(5(x1)))))) 60.02/16.10 1(0(3(5(4(x1))))) -> 1(0(3(1(4(5(x1)))))) 60.02/16.10 1(0(3(5(4(x1))))) -> 0(2(3(1(4(5(x1)))))) 60.02/16.10 1(0(3(5(4(x1))))) -> 1(2(0(3(4(5(x1)))))) 60.02/16.10 1(1(3(5(4(x1))))) -> 5(1(3(1(4(2(x1)))))) 60.02/16.10 1(1(3(5(4(x1))))) -> 1(3(1(2(5(4(x1)))))) 60.02/16.10 1(1(3(5(4(x1))))) -> 2(1(4(3(1(5(x1)))))) 60.02/16.10 1(1(3(5(4(x1))))) -> 3(1(4(1(2(5(x1)))))) 60.02/16.10 1(1(3(5(4(x1))))) -> 1(3(1(2(4(5(x1)))))) 60.02/16.10 1(1(5(5(4(x1))))) -> 4(1(1(2(5(5(x1)))))) 60.02/16.10 1(1(5(5(4(x1))))) -> 1(1(4(2(5(5(x1)))))) 60.02/16.10 60.02/16.10 Q is empty. 60.02/16.10 We have to consider all minimal (P,Q,R)-chains. 60.02/16.10 ---------------------------------------- 60.02/16.10 60.02/16.10 (5) DependencyGraphProof (EQUIVALENT) 60.02/16.10 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 185 less nodes. 60.02/16.10 ---------------------------------------- 60.02/16.10 60.02/16.10 (6) 60.02/16.10 Obligation: 60.02/16.10 Q DP problem: 60.02/16.10 The TRS P consists of the following rules: 60.02/16.10 60.02/16.10 1^1(0(3(4(x1)))) -> 1^1(x1) 60.02/16.10 1^1(0(1(4(x1)))) -> 1^1(x1) 60.02/16.10 1^1(1(0(1(4(x1))))) -> 1^1(x1) 60.02/16.10 1^1(0(2(1(4(x1))))) -> 1^1(x1) 60.02/16.10 1^1(0(5(1(4(x1))))) -> 1^1(1(x1)) 60.02/16.10 1^1(0(5(1(4(x1))))) -> 1^1(x1) 60.02/16.10 1^1(1(5(1(4(x1))))) -> 1^1(x1) 60.02/16.10 1^1(1(0(3(4(x1))))) -> 1^1(x1) 60.02/16.10 1^1(0(1(3(4(x1))))) -> 1^1(x1) 60.02/16.10 1^1(1(2(3(4(x1))))) -> 1^1(x1) 60.02/16.10 1^1(0(5(3(4(x1))))) -> 1^1(x1) 60.02/16.10 1^1(1(5(3(4(x1))))) -> 1^1(x1) 60.02/16.10 1^1(0(1(5(4(x1))))) -> 1^1(x1) 60.02/16.10 1^1(0(3(5(4(x1))))) -> 1^1(x1) 60.02/16.10 60.02/16.10 The TRS R consists of the following rules: 60.02/16.10 60.02/16.10 1(0(1(0(x1)))) -> 1(3(1(2(0(0(x1)))))) 60.02/16.10 1(0(1(0(x1)))) -> 1(0(2(0(1(2(x1)))))) 60.02/16.10 1(0(1(0(x1)))) -> 0(0(1(3(1(2(x1)))))) 60.02/16.10 1(0(1(4(x1)))) -> 1(2(4(0(1(x1))))) 60.02/16.10 1(0(1(4(x1)))) -> 1(2(0(1(4(x1))))) 60.02/16.10 1(0(1(4(x1)))) -> 1(4(3(1(2(0(x1)))))) 60.02/16.10 1(0(1(4(x1)))) -> 1(3(1(2(4(0(x1)))))) 60.02/16.10 1(0(1(4(x1)))) -> 3(1(4(2(0(1(x1)))))) 60.02/16.10 1(0(1(4(x1)))) -> 1(2(2(4(0(1(x1)))))) 60.02/16.10 1(0(1(4(x1)))) -> 1(2(5(4(0(1(x1)))))) 60.02/16.10 1(0(1(4(x1)))) -> 1(3(1(2(0(4(x1)))))) 60.02/16.10 1(0(1(4(x1)))) -> 3(1(2(0(1(4(x1)))))) 60.02/16.10 1(0(1(4(x1)))) -> 1(2(0(3(1(4(x1)))))) 60.02/16.10 1(1(1(4(x1)))) -> 1(3(1(3(1(4(x1)))))) 60.02/16.10 1(0(3(4(x1)))) -> 4(3(1(2(0(x1))))) 60.02/16.10 1(0(3(4(x1)))) -> 3(1(4(2(0(x1))))) 60.02/16.10 1(0(3(4(x1)))) -> 3(1(2(4(0(x1))))) 60.02/16.10 1(0(3(4(x1)))) -> 1(2(4(0(3(x1))))) 60.02/16.10 1(0(3(4(x1)))) -> 1(2(0(4(3(x1))))) 60.02/16.10 1(0(3(4(x1)))) -> 3(1(2(0(4(x1))))) 60.02/16.10 1(0(3(4(x1)))) -> 1(2(0(3(4(x1))))) 60.02/16.10 1(0(3(4(x1)))) -> 4(3(3(1(2(0(x1)))))) 60.02/16.10 1(0(3(4(x1)))) -> 3(4(3(1(2(0(x1)))))) 60.02/16.10 1(0(3(4(x1)))) -> 3(3(1(4(2(0(x1)))))) 60.02/16.10 1(0(3(4(x1)))) -> 3(1(2(2(4(0(x1)))))) 60.02/16.10 1(0(3(4(x1)))) -> 3(1(2(5(4(0(x1)))))) 60.02/16.10 1(0(3(4(x1)))) -> 4(3(1(2(0(1(x1)))))) 60.02/16.10 1(0(3(4(x1)))) -> 3(1(4(2(0(1(x1)))))) 60.02/16.10 1(0(3(4(x1)))) -> 3(1(2(4(0(1(x1)))))) 60.02/16.10 1(0(3(4(x1)))) -> 1(2(4(0(3(1(x1)))))) 60.02/16.10 1(0(3(4(x1)))) -> 1(2(5(4(0(3(x1)))))) 60.02/16.10 1(0(3(4(x1)))) -> 1(2(4(0(1(3(x1)))))) 60.02/16.10 1(0(3(4(x1)))) -> 1(2(0(4(3(3(x1)))))) 60.02/16.10 1(0(3(4(x1)))) -> 3(1(2(0(4(3(x1)))))) 60.02/16.10 1(0(3(4(x1)))) -> 1(2(2(0(4(3(x1)))))) 60.02/16.10 1(0(3(4(x1)))) -> 1(2(5(0(4(3(x1)))))) 60.02/16.10 1(0(3(4(x1)))) -> 1(2(0(1(4(3(x1)))))) 60.02/16.10 1(0(3(4(x1)))) -> 1(2(0(3(4(3(x1)))))) 60.02/16.10 1(0(3(4(x1)))) -> 3(1(2(0(3(4(x1)))))) 60.02/16.10 1(0(3(4(x1)))) -> 1(2(5(0(3(4(x1)))))) 60.02/16.10 1(0(3(4(x1)))) -> 1(2(0(1(3(4(x1)))))) 60.02/16.10 1(0(3(4(x1)))) -> 1(2(0(3(3(4(x1)))))) 60.02/16.10 1(1(5(4(x1)))) -> 1(1(2(5(4(x1))))) 60.02/16.10 1(1(5(4(x1)))) -> 1(1(2(5(2(4(x1)))))) 60.02/16.10 1(1(5(4(x1)))) -> 1(3(1(2(5(4(x1)))))) 60.02/16.10 1(1(5(4(x1)))) -> 1(1(2(2(5(4(x1)))))) 60.02/16.10 1(1(5(4(x1)))) -> 1(1(2(5(5(4(x1)))))) 60.02/16.10 1(0(1(0(0(x1))))) -> 1(2(0(1(0(0(x1)))))) 60.02/16.10 1(1(3(0(0(x1))))) -> 0(0(1(3(1(2(x1)))))) 60.02/16.10 1(1(5(0(0(x1))))) -> 1(1(2(0(0(5(x1)))))) 60.02/16.10 1(0(1(4(0(x1))))) -> 1(0(4(0(1(2(x1)))))) 60.02/16.10 1(0(3(4(0(x1))))) -> 4(3(1(2(0(0(x1)))))) 60.02/16.10 1(0(3(4(0(x1))))) -> 1(2(0(3(4(0(x1)))))) 60.02/16.10 1(0(3(4(0(x1))))) -> 0(4(0(1(3(2(x1)))))) 60.02/16.10 1(1(3(4(0(x1))))) -> 0(3(1(4(1(2(x1)))))) 60.02/16.10 1(1(3(4(0(x1))))) -> 1(1(3(0(2(4(x1)))))) 60.02/16.10 1(1(5(4(0(x1))))) -> 1(2(5(1(0(4(x1)))))) 60.02/16.10 1(1(5(4(0(x1))))) -> 1(0(4(1(2(5(x1)))))) 60.02/16.10 1(0(3(0(4(x1))))) -> 3(1(2(4(0(0(x1)))))) 60.02/16.10 1(0(3(0(4(x1))))) -> 3(1(0(4(0(2(x1)))))) 60.02/16.10 1(0(3(0(4(x1))))) -> 1(3(0(4(0(2(x1)))))) 60.02/16.10 1(1(0(1(4(x1))))) -> 1(1(2(4(0(1(x1)))))) 60.02/16.10 1(0(1(1(4(x1))))) -> 1(1(2(0(1(4(x1)))))) 60.02/16.10 1(0(2(1(4(x1))))) -> 1(3(1(2(4(0(x1)))))) 60.02/16.10 1(0(2(1(4(x1))))) -> 3(1(4(2(0(1(x1)))))) 60.02/16.10 1(0(2(1(4(x1))))) -> 1(1(2(2(0(4(x1)))))) 60.02/16.10 1(0(2(1(4(x1))))) -> 1(2(2(0(1(4(x1)))))) 60.02/16.10 1(0(3(1(4(x1))))) -> 1(2(0(3(1(4(x1)))))) 60.02/16.10 1(0(5(1(4(x1))))) -> 2(4(0(5(1(1(x1)))))) 60.02/16.10 1(1(5(1(4(x1))))) -> 1(1(2(5(4(1(x1)))))) 60.02/16.10 1(1(0(3(4(x1))))) -> 4(1(2(0(3(1(x1)))))) 60.02/16.10 1(1(0(3(4(x1))))) -> 2(0(4(1(3(1(x1)))))) 60.02/16.10 1(1(0(3(4(x1))))) -> 0(2(4(1(3(1(x1)))))) 60.02/16.10 1(1(0(3(4(x1))))) -> 1(4(2(0(1(3(x1)))))) 60.02/16.10 1(1(0(3(4(x1))))) -> 2(0(1(1(3(4(x1)))))) 60.02/16.10 1(0(1(3(4(x1))))) -> 1(3(1(2(4(0(x1)))))) 60.02/16.10 1(0(1(3(4(x1))))) -> 1(2(0(4(3(1(x1)))))) 60.02/16.10 1(0(2(3(4(x1))))) -> 1(2(2(0(4(3(x1)))))) 60.02/16.10 1(0(2(3(4(x1))))) -> 1(2(5(0(4(3(x1)))))) 60.02/16.10 1(0(2(3(4(x1))))) -> 1(3(1(2(0(4(x1)))))) 60.02/16.10 1(0(2(3(4(x1))))) -> 3(1(2(0(3(4(x1)))))) 60.02/16.10 1(1(2(3(4(x1))))) -> 2(4(2(1(3(1(x1)))))) 60.02/16.10 1(1(2(3(4(x1))))) -> 2(5(4(1(3(1(x1)))))) 60.02/16.10 1(1(2(3(4(x1))))) -> 2(1(4(3(1(3(x1)))))) 60.02/16.10 1(1(2(3(4(x1))))) -> 2(2(1(3(1(4(x1)))))) 60.02/16.10 1(1(2(3(4(x1))))) -> 2(1(3(3(1(4(x1)))))) 60.02/16.10 1(0(3(3(4(x1))))) -> 1(2(0(3(3(4(x1)))))) 60.02/16.10 1(0(4(3(4(x1))))) -> 1(2(4(0(4(3(x1)))))) 60.02/16.10 1(0(4(3(4(x1))))) -> 3(1(2(0(4(4(x1)))))) 60.02/16.10 1(0(5(3(4(x1))))) -> 4(1(3(2(5(0(x1)))))) 60.02/16.10 1(0(5(3(4(x1))))) -> 4(5(2(0(3(1(x1)))))) 60.02/16.10 1(0(5(3(4(x1))))) -> 5(2(4(0(3(1(x1)))))) 60.02/16.10 1(0(5(3(4(x1))))) -> 2(5(0(4(3(1(x1)))))) 60.02/16.10 1(0(5(3(4(x1))))) -> 5(2(4(0(1(3(x1)))))) 60.02/16.10 1(0(5(3(4(x1))))) -> 2(4(0(5(1(3(x1)))))) 60.02/16.10 1(0(5(3(4(x1))))) -> 5(1(2(0(4(3(x1)))))) 60.02/16.10 1(0(5(3(4(x1))))) -> 2(0(5(1(4(3(x1)))))) 60.02/16.10 1(0(5(3(4(x1))))) -> 2(4(0(1(5(3(x1)))))) 60.02/16.10 1(0(5(3(4(x1))))) -> 5(1(2(0(3(4(x1)))))) 60.02/16.10 1(0(5(3(4(x1))))) -> 2(0(4(3(1(5(x1)))))) 60.02/16.10 1(1(5(3(4(x1))))) -> 3(1(2(5(4(1(x1)))))) 60.02/16.10 1(1(5(3(4(x1))))) -> 2(4(5(1(1(3(x1)))))) 60.02/16.10 1(1(5(3(4(x1))))) -> 1(2(5(4(1(3(x1)))))) 60.02/16.10 1(1(5(3(4(x1))))) -> 5(3(1(3(1(4(x1)))))) 60.02/16.10 1(1(5(3(4(x1))))) -> 3(1(2(5(1(4(x1)))))) 60.02/16.10 1(1(5(3(4(x1))))) -> 1(2(5(1(3(4(x1)))))) 60.02/16.10 1(0(1(4(4(x1))))) -> 1(2(0(1(4(4(x1)))))) 60.02/16.10 1(0(3(4(4(x1))))) -> 3(1(2(4(4(0(x1)))))) 60.02/16.10 1(0(3(4(4(x1))))) -> 4(3(1(2(0(4(x1)))))) 60.02/16.10 1(0(3(4(4(x1))))) -> 1(2(0(4(3(4(x1)))))) 60.02/16.10 1(0(3(4(4(x1))))) -> 1(2(0(3(4(4(x1)))))) 60.02/16.10 1(0(1(5(4(x1))))) -> 1(4(3(1(5(0(x1)))))) 60.02/16.10 1(0(1(5(4(x1))))) -> 1(3(1(4(5(0(x1)))))) 60.02/16.10 1(0(1(5(4(x1))))) -> 1(2(5(4(0(1(x1)))))) 60.02/16.10 1(0(1(5(4(x1))))) -> 1(1(2(5(0(4(x1)))))) 60.02/16.10 1(0(1(5(4(x1))))) -> 1(2(0(1(5(4(x1)))))) 60.02/16.10 1(0(1(5(4(x1))))) -> 1(4(2(0(1(5(x1)))))) 60.02/16.10 1(0(1(5(4(x1))))) -> 1(2(0(1(4(5(x1)))))) 60.02/16.10 1(1(1(5(4(x1))))) -> 1(1(1(2(5(4(x1)))))) 60.02/16.10 1(0(3(5(4(x1))))) -> 5(4(3(1(2(0(x1)))))) 60.02/16.10 1(0(3(5(4(x1))))) -> 4(3(1(2(5(0(x1)))))) 60.02/16.10 1(0(3(5(4(x1))))) -> 1(3(4(2(5(0(x1)))))) 60.02/16.10 1(0(3(5(4(x1))))) -> 3(1(2(4(5(0(x1)))))) 60.02/16.10 1(0(3(5(4(x1))))) -> 4(3(1(5(0(1(x1)))))) 60.02/16.10 1(0(3(5(4(x1))))) -> 4(3(3(0(5(1(x1)))))) 60.02/16.10 1(0(3(5(4(x1))))) -> 3(0(5(4(1(2(x1)))))) 60.02/16.10 1(0(3(5(4(x1))))) -> 0(5(3(1(4(2(x1)))))) 60.02/16.10 1(0(3(5(4(x1))))) -> 1(2(5(4(0(3(x1)))))) 60.02/16.10 1(0(3(5(4(x1))))) -> 2(5(1(3(0(4(x1)))))) 60.02/16.10 1(0(3(5(4(x1))))) -> 1(5(3(3(0(4(x1)))))) 60.02/16.10 1(0(3(5(4(x1))))) -> 3(1(4(5(0(4(x1)))))) 60.02/16.10 1(0(3(5(4(x1))))) -> 3(0(5(3(1(4(x1)))))) 60.02/16.10 1(0(3(5(4(x1))))) -> 0(5(5(3(1(4(x1)))))) 60.02/16.10 1(0(3(5(4(x1))))) -> 1(3(0(5(2(4(x1)))))) 60.02/16.10 1(0(3(5(4(x1))))) -> 1(3(0(2(5(4(x1)))))) 60.02/16.10 1(0(3(5(4(x1))))) -> 1(4(1(3(0(5(x1)))))) 60.02/16.10 1(0(3(5(4(x1))))) -> 1(4(4(3(0(5(x1)))))) 60.02/16.10 1(0(3(5(4(x1))))) -> 4(3(0(3(1(5(x1)))))) 60.02/16.10 1(0(3(5(4(x1))))) -> 0(4(3(1(2(5(x1)))))) 60.02/16.10 1(0(3(5(4(x1))))) -> 0(3(1(4(2(5(x1)))))) 60.02/16.10 1(0(3(5(4(x1))))) -> 1(2(4(0(3(5(x1)))))) 60.02/16.10 1(0(3(5(4(x1))))) -> 1(0(3(1(4(5(x1)))))) 60.02/16.10 1(0(3(5(4(x1))))) -> 0(2(3(1(4(5(x1)))))) 60.02/16.10 1(0(3(5(4(x1))))) -> 1(2(0(3(4(5(x1)))))) 60.02/16.10 1(1(3(5(4(x1))))) -> 5(1(3(1(4(2(x1)))))) 60.02/16.10 1(1(3(5(4(x1))))) -> 1(3(1(2(5(4(x1)))))) 60.02/16.10 1(1(3(5(4(x1))))) -> 2(1(4(3(1(5(x1)))))) 60.02/16.10 1(1(3(5(4(x1))))) -> 3(1(4(1(2(5(x1)))))) 60.02/16.10 1(1(3(5(4(x1))))) -> 1(3(1(2(4(5(x1)))))) 60.02/16.10 1(1(5(5(4(x1))))) -> 4(1(1(2(5(5(x1)))))) 60.02/16.10 1(1(5(5(4(x1))))) -> 1(1(4(2(5(5(x1)))))) 60.02/16.10 60.02/16.10 Q is empty. 60.02/16.10 We have to consider all minimal (P,Q,R)-chains. 60.02/16.10 ---------------------------------------- 60.02/16.10 60.02/16.10 (7) QDPOrderProof (EQUIVALENT) 60.02/16.10 We use the reduction pair processor [LPAR04,JAR06]. 60.02/16.10 60.02/16.10 60.02/16.10 The following pairs can be oriented strictly and are deleted. 60.02/16.10 60.02/16.10 1^1(0(3(4(x1)))) -> 1^1(x1) 60.02/16.10 1^1(0(1(4(x1)))) -> 1^1(x1) 60.02/16.10 1^1(1(0(1(4(x1))))) -> 1^1(x1) 60.02/16.10 1^1(0(2(1(4(x1))))) -> 1^1(x1) 60.02/16.10 1^1(0(5(1(4(x1))))) -> 1^1(1(x1)) 60.02/16.10 1^1(0(5(1(4(x1))))) -> 1^1(x1) 60.02/16.10 1^1(1(0(3(4(x1))))) -> 1^1(x1) 60.02/16.10 1^1(0(1(3(4(x1))))) -> 1^1(x1) 60.02/16.10 1^1(0(5(3(4(x1))))) -> 1^1(x1) 60.02/16.10 1^1(0(1(5(4(x1))))) -> 1^1(x1) 60.02/16.10 1^1(0(3(5(4(x1))))) -> 1^1(x1) 60.02/16.10 The remaining pairs can at least be oriented weakly. 60.02/16.10 Used ordering: Polynomial interpretation [POLO]: 60.02/16.10 60.02/16.10 POL(0(x_1)) = 1 + x_1 60.02/16.10 POL(1(x_1)) = x_1 60.02/16.10 POL(1^1(x_1)) = x_1 60.02/16.10 POL(2(x_1)) = x_1 60.02/16.10 POL(3(x_1)) = x_1 60.02/16.10 POL(4(x_1)) = x_1 60.02/16.10 POL(5(x_1)) = x_1 60.02/16.10 60.02/16.10 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 60.02/16.10 60.02/16.10 1(0(1(0(x1)))) -> 1(3(1(2(0(0(x1)))))) 60.02/16.10 1(0(1(0(x1)))) -> 1(0(2(0(1(2(x1)))))) 60.02/16.10 1(0(1(0(x1)))) -> 0(0(1(3(1(2(x1)))))) 60.02/16.10 1(0(1(4(x1)))) -> 1(2(4(0(1(x1))))) 60.02/16.10 1(0(1(4(x1)))) -> 1(2(0(1(4(x1))))) 60.02/16.10 1(0(1(4(x1)))) -> 1(4(3(1(2(0(x1)))))) 60.02/16.10 1(0(1(4(x1)))) -> 1(3(1(2(4(0(x1)))))) 60.02/16.10 1(0(1(4(x1)))) -> 3(1(4(2(0(1(x1)))))) 60.02/16.10 1(0(1(4(x1)))) -> 1(2(2(4(0(1(x1)))))) 60.02/16.10 1(0(1(4(x1)))) -> 1(2(5(4(0(1(x1)))))) 60.02/16.10 1(0(1(4(x1)))) -> 1(3(1(2(0(4(x1)))))) 60.02/16.10 1(0(1(4(x1)))) -> 3(1(2(0(1(4(x1)))))) 60.02/16.10 1(0(1(4(x1)))) -> 1(2(0(3(1(4(x1)))))) 60.02/16.10 1(1(1(4(x1)))) -> 1(3(1(3(1(4(x1)))))) 60.02/16.10 1(0(3(4(x1)))) -> 4(3(1(2(0(x1))))) 60.02/16.10 1(0(3(4(x1)))) -> 3(1(4(2(0(x1))))) 60.02/16.10 1(0(3(4(x1)))) -> 3(1(2(4(0(x1))))) 60.02/16.10 1(0(3(4(x1)))) -> 1(2(4(0(3(x1))))) 60.02/16.10 1(0(3(4(x1)))) -> 1(2(0(4(3(x1))))) 60.02/16.10 1(0(3(4(x1)))) -> 3(1(2(0(4(x1))))) 60.02/16.10 1(0(3(4(x1)))) -> 1(2(0(3(4(x1))))) 60.02/16.10 1(0(3(4(x1)))) -> 4(3(3(1(2(0(x1)))))) 60.02/16.10 1(0(3(4(x1)))) -> 3(4(3(1(2(0(x1)))))) 60.02/16.10 1(0(3(4(x1)))) -> 3(3(1(4(2(0(x1)))))) 60.02/16.10 1(0(3(4(x1)))) -> 3(1(2(2(4(0(x1)))))) 60.02/16.10 1(0(3(4(x1)))) -> 3(1(2(5(4(0(x1)))))) 60.02/16.10 1(0(3(4(x1)))) -> 4(3(1(2(0(1(x1)))))) 60.02/16.10 1(0(3(4(x1)))) -> 3(1(4(2(0(1(x1)))))) 60.02/16.10 1(0(3(4(x1)))) -> 3(1(2(4(0(1(x1)))))) 60.02/16.10 1(0(3(4(x1)))) -> 1(2(4(0(3(1(x1)))))) 60.02/16.10 1(0(3(4(x1)))) -> 1(2(5(4(0(3(x1)))))) 60.02/16.10 1(0(3(4(x1)))) -> 1(2(4(0(1(3(x1)))))) 60.02/16.10 1(0(3(4(x1)))) -> 1(2(0(4(3(3(x1)))))) 60.02/16.10 1(0(3(4(x1)))) -> 3(1(2(0(4(3(x1)))))) 60.02/16.10 1(0(3(4(x1)))) -> 1(2(2(0(4(3(x1)))))) 60.02/16.10 1(0(3(4(x1)))) -> 1(2(5(0(4(3(x1)))))) 60.02/16.10 1(0(3(4(x1)))) -> 1(2(0(1(4(3(x1)))))) 60.02/16.10 1(0(3(4(x1)))) -> 1(2(0(3(4(3(x1)))))) 60.02/16.10 1(0(3(4(x1)))) -> 3(1(2(0(3(4(x1)))))) 60.02/16.10 1(0(3(4(x1)))) -> 1(2(5(0(3(4(x1)))))) 60.02/16.10 1(0(3(4(x1)))) -> 1(2(0(1(3(4(x1)))))) 60.02/16.10 1(0(3(4(x1)))) -> 1(2(0(3(3(4(x1)))))) 60.02/16.10 1(1(5(4(x1)))) -> 1(1(2(5(4(x1))))) 60.02/16.10 1(1(5(4(x1)))) -> 1(1(2(5(2(4(x1)))))) 60.02/16.10 1(1(5(4(x1)))) -> 1(3(1(2(5(4(x1)))))) 60.02/16.10 1(1(5(4(x1)))) -> 1(1(2(2(5(4(x1)))))) 60.02/16.10 1(1(5(4(x1)))) -> 1(1(2(5(5(4(x1)))))) 60.02/16.10 1(0(1(0(0(x1))))) -> 1(2(0(1(0(0(x1)))))) 60.02/16.10 1(1(3(0(0(x1))))) -> 0(0(1(3(1(2(x1)))))) 60.02/16.10 1(1(5(0(0(x1))))) -> 1(1(2(0(0(5(x1)))))) 60.02/16.10 1(0(1(4(0(x1))))) -> 1(0(4(0(1(2(x1)))))) 60.02/16.10 1(0(3(4(0(x1))))) -> 4(3(1(2(0(0(x1)))))) 60.02/16.10 1(0(3(4(0(x1))))) -> 1(2(0(3(4(0(x1)))))) 60.02/16.10 1(0(3(4(0(x1))))) -> 0(4(0(1(3(2(x1)))))) 60.02/16.10 1(1(3(4(0(x1))))) -> 0(3(1(4(1(2(x1)))))) 60.02/16.10 1(1(3(4(0(x1))))) -> 1(1(3(0(2(4(x1)))))) 60.02/16.10 1(1(5(4(0(x1))))) -> 1(2(5(1(0(4(x1)))))) 60.02/16.10 1(1(5(4(0(x1))))) -> 1(0(4(1(2(5(x1)))))) 60.02/16.10 1(0(3(0(4(x1))))) -> 3(1(2(4(0(0(x1)))))) 60.02/16.10 1(0(3(0(4(x1))))) -> 3(1(0(4(0(2(x1)))))) 60.02/16.10 1(0(3(0(4(x1))))) -> 1(3(0(4(0(2(x1)))))) 60.02/16.10 1(1(0(1(4(x1))))) -> 1(1(2(4(0(1(x1)))))) 60.02/16.10 1(0(1(1(4(x1))))) -> 1(1(2(0(1(4(x1)))))) 60.02/16.10 1(0(2(1(4(x1))))) -> 1(3(1(2(4(0(x1)))))) 60.02/16.10 1(0(2(1(4(x1))))) -> 3(1(4(2(0(1(x1)))))) 60.02/16.10 1(0(2(1(4(x1))))) -> 1(1(2(2(0(4(x1)))))) 60.02/16.10 1(0(2(1(4(x1))))) -> 1(2(2(0(1(4(x1)))))) 60.02/16.10 1(0(3(1(4(x1))))) -> 1(2(0(3(1(4(x1)))))) 60.02/16.10 1(0(5(1(4(x1))))) -> 2(4(0(5(1(1(x1)))))) 60.02/16.10 1(1(5(1(4(x1))))) -> 1(1(2(5(4(1(x1)))))) 60.02/16.10 1(1(0(3(4(x1))))) -> 4(1(2(0(3(1(x1)))))) 60.02/16.10 1(1(0(3(4(x1))))) -> 2(0(4(1(3(1(x1)))))) 60.02/16.10 1(1(0(3(4(x1))))) -> 0(2(4(1(3(1(x1)))))) 60.02/16.10 1(1(0(3(4(x1))))) -> 1(4(2(0(1(3(x1)))))) 60.02/16.10 1(1(0(3(4(x1))))) -> 2(0(1(1(3(4(x1)))))) 60.02/16.10 1(0(1(3(4(x1))))) -> 1(3(1(2(4(0(x1)))))) 60.02/16.10 1(0(1(3(4(x1))))) -> 1(2(0(4(3(1(x1)))))) 60.02/16.10 1(0(2(3(4(x1))))) -> 1(2(2(0(4(3(x1)))))) 60.02/16.10 1(0(2(3(4(x1))))) -> 1(2(5(0(4(3(x1)))))) 60.02/16.10 1(0(2(3(4(x1))))) -> 1(3(1(2(0(4(x1)))))) 60.02/16.10 1(0(2(3(4(x1))))) -> 3(1(2(0(3(4(x1)))))) 60.02/16.10 1(1(2(3(4(x1))))) -> 2(4(2(1(3(1(x1)))))) 60.02/16.10 1(1(2(3(4(x1))))) -> 2(5(4(1(3(1(x1)))))) 60.02/16.10 1(1(2(3(4(x1))))) -> 2(1(4(3(1(3(x1)))))) 60.02/16.10 1(1(2(3(4(x1))))) -> 2(2(1(3(1(4(x1)))))) 60.02/16.10 1(1(2(3(4(x1))))) -> 2(1(3(3(1(4(x1)))))) 60.02/16.10 1(0(3(3(4(x1))))) -> 1(2(0(3(3(4(x1)))))) 60.02/16.10 1(0(4(3(4(x1))))) -> 1(2(4(0(4(3(x1)))))) 60.02/16.10 1(0(4(3(4(x1))))) -> 3(1(2(0(4(4(x1)))))) 60.02/16.10 1(0(5(3(4(x1))))) -> 4(1(3(2(5(0(x1)))))) 60.02/16.10 1(0(5(3(4(x1))))) -> 4(5(2(0(3(1(x1)))))) 60.02/16.10 1(0(5(3(4(x1))))) -> 5(2(4(0(3(1(x1)))))) 60.02/16.10 1(0(5(3(4(x1))))) -> 2(5(0(4(3(1(x1)))))) 60.02/16.10 1(0(5(3(4(x1))))) -> 5(2(4(0(1(3(x1)))))) 60.02/16.10 1(0(5(3(4(x1))))) -> 2(4(0(5(1(3(x1)))))) 60.02/16.10 1(0(5(3(4(x1))))) -> 5(1(2(0(4(3(x1)))))) 60.02/16.10 1(0(5(3(4(x1))))) -> 2(0(5(1(4(3(x1)))))) 60.02/16.10 1(0(5(3(4(x1))))) -> 2(4(0(1(5(3(x1)))))) 60.02/16.10 1(0(5(3(4(x1))))) -> 5(1(2(0(3(4(x1)))))) 60.02/16.10 1(0(5(3(4(x1))))) -> 2(0(4(3(1(5(x1)))))) 60.02/16.10 1(1(5(3(4(x1))))) -> 3(1(2(5(4(1(x1)))))) 60.02/16.10 1(1(5(3(4(x1))))) -> 2(4(5(1(1(3(x1)))))) 60.02/16.10 1(1(5(3(4(x1))))) -> 1(2(5(4(1(3(x1)))))) 60.02/16.10 1(1(5(3(4(x1))))) -> 5(3(1(3(1(4(x1)))))) 60.02/16.10 1(1(5(3(4(x1))))) -> 3(1(2(5(1(4(x1)))))) 60.02/16.10 1(1(5(3(4(x1))))) -> 1(2(5(1(3(4(x1)))))) 60.02/16.10 1(0(1(4(4(x1))))) -> 1(2(0(1(4(4(x1)))))) 60.02/16.10 1(0(3(4(4(x1))))) -> 3(1(2(4(4(0(x1)))))) 60.02/16.10 1(0(3(4(4(x1))))) -> 4(3(1(2(0(4(x1)))))) 60.02/16.10 1(0(3(4(4(x1))))) -> 1(2(0(4(3(4(x1)))))) 60.02/16.10 1(0(3(4(4(x1))))) -> 1(2(0(3(4(4(x1)))))) 60.02/16.10 1(0(1(5(4(x1))))) -> 1(4(3(1(5(0(x1)))))) 60.02/16.10 1(0(1(5(4(x1))))) -> 1(3(1(4(5(0(x1)))))) 60.02/16.10 1(0(1(5(4(x1))))) -> 1(2(5(4(0(1(x1)))))) 60.02/16.10 1(0(1(5(4(x1))))) -> 1(1(2(5(0(4(x1)))))) 60.02/16.10 1(0(1(5(4(x1))))) -> 1(2(0(1(5(4(x1)))))) 60.02/16.10 1(0(1(5(4(x1))))) -> 1(4(2(0(1(5(x1)))))) 60.02/16.10 1(0(1(5(4(x1))))) -> 1(2(0(1(4(5(x1)))))) 60.02/16.10 1(1(1(5(4(x1))))) -> 1(1(1(2(5(4(x1)))))) 60.02/16.10 1(0(3(5(4(x1))))) -> 5(4(3(1(2(0(x1)))))) 60.02/16.10 1(0(3(5(4(x1))))) -> 4(3(1(2(5(0(x1)))))) 60.02/16.10 1(0(3(5(4(x1))))) -> 1(3(4(2(5(0(x1)))))) 60.02/16.10 1(0(3(5(4(x1))))) -> 3(1(2(4(5(0(x1)))))) 60.02/16.10 1(0(3(5(4(x1))))) -> 4(3(1(5(0(1(x1)))))) 60.02/16.10 1(0(3(5(4(x1))))) -> 4(3(3(0(5(1(x1)))))) 60.02/16.10 1(0(3(5(4(x1))))) -> 3(0(5(4(1(2(x1)))))) 60.02/16.10 1(0(3(5(4(x1))))) -> 0(5(3(1(4(2(x1)))))) 60.02/16.10 1(0(3(5(4(x1))))) -> 1(2(5(4(0(3(x1)))))) 60.02/16.10 1(0(3(5(4(x1))))) -> 2(5(1(3(0(4(x1)))))) 60.02/16.10 1(0(3(5(4(x1))))) -> 1(5(3(3(0(4(x1)))))) 60.02/16.10 1(0(3(5(4(x1))))) -> 3(1(4(5(0(4(x1)))))) 60.02/16.10 1(0(3(5(4(x1))))) -> 3(0(5(3(1(4(x1)))))) 60.02/16.10 1(0(3(5(4(x1))))) -> 0(5(5(3(1(4(x1)))))) 60.02/16.10 1(0(3(5(4(x1))))) -> 1(3(0(5(2(4(x1)))))) 60.02/16.10 1(0(3(5(4(x1))))) -> 1(3(0(2(5(4(x1)))))) 60.02/16.10 1(0(3(5(4(x1))))) -> 1(4(1(3(0(5(x1)))))) 60.02/16.10 1(0(3(5(4(x1))))) -> 1(4(4(3(0(5(x1)))))) 60.02/16.10 1(0(3(5(4(x1))))) -> 4(3(0(3(1(5(x1)))))) 60.02/16.10 1(0(3(5(4(x1))))) -> 0(4(3(1(2(5(x1)))))) 60.02/16.10 1(0(3(5(4(x1))))) -> 0(3(1(4(2(5(x1)))))) 60.02/16.10 1(0(3(5(4(x1))))) -> 1(2(4(0(3(5(x1)))))) 60.02/16.10 1(0(3(5(4(x1))))) -> 1(0(3(1(4(5(x1)))))) 60.02/16.10 1(0(3(5(4(x1))))) -> 0(2(3(1(4(5(x1)))))) 60.02/16.10 1(0(3(5(4(x1))))) -> 1(2(0(3(4(5(x1)))))) 60.02/16.10 1(1(3(5(4(x1))))) -> 5(1(3(1(4(2(x1)))))) 60.02/16.10 1(1(3(5(4(x1))))) -> 1(3(1(2(5(4(x1)))))) 60.02/16.10 1(1(3(5(4(x1))))) -> 2(1(4(3(1(5(x1)))))) 60.02/16.10 1(1(3(5(4(x1))))) -> 3(1(4(1(2(5(x1)))))) 60.02/16.10 1(1(3(5(4(x1))))) -> 1(3(1(2(4(5(x1)))))) 60.02/16.10 1(1(5(5(4(x1))))) -> 4(1(1(2(5(5(x1)))))) 60.02/16.10 1(1(5(5(4(x1))))) -> 1(1(4(2(5(5(x1)))))) 60.02/16.10 60.02/16.10 60.02/16.10 ---------------------------------------- 60.02/16.10 60.02/16.10 (8) 60.02/16.10 Obligation: 60.02/16.10 Q DP problem: 60.02/16.10 The TRS P consists of the following rules: 60.02/16.10 60.02/16.10 1^1(1(5(1(4(x1))))) -> 1^1(x1) 60.02/16.10 1^1(1(2(3(4(x1))))) -> 1^1(x1) 60.02/16.10 1^1(1(5(3(4(x1))))) -> 1^1(x1) 60.02/16.10 60.02/16.10 The TRS R consists of the following rules: 60.02/16.10 60.02/16.10 1(0(1(0(x1)))) -> 1(3(1(2(0(0(x1)))))) 60.02/16.10 1(0(1(0(x1)))) -> 1(0(2(0(1(2(x1)))))) 60.02/16.10 1(0(1(0(x1)))) -> 0(0(1(3(1(2(x1)))))) 60.02/16.10 1(0(1(4(x1)))) -> 1(2(4(0(1(x1))))) 60.02/16.10 1(0(1(4(x1)))) -> 1(2(0(1(4(x1))))) 60.02/16.10 1(0(1(4(x1)))) -> 1(4(3(1(2(0(x1)))))) 60.02/16.10 1(0(1(4(x1)))) -> 1(3(1(2(4(0(x1)))))) 60.02/16.10 1(0(1(4(x1)))) -> 3(1(4(2(0(1(x1)))))) 60.02/16.10 1(0(1(4(x1)))) -> 1(2(2(4(0(1(x1)))))) 60.02/16.10 1(0(1(4(x1)))) -> 1(2(5(4(0(1(x1)))))) 60.02/16.10 1(0(1(4(x1)))) -> 1(3(1(2(0(4(x1)))))) 60.02/16.10 1(0(1(4(x1)))) -> 3(1(2(0(1(4(x1)))))) 60.02/16.10 1(0(1(4(x1)))) -> 1(2(0(3(1(4(x1)))))) 60.02/16.10 1(1(1(4(x1)))) -> 1(3(1(3(1(4(x1)))))) 60.02/16.10 1(0(3(4(x1)))) -> 4(3(1(2(0(x1))))) 60.02/16.10 1(0(3(4(x1)))) -> 3(1(4(2(0(x1))))) 60.02/16.10 1(0(3(4(x1)))) -> 3(1(2(4(0(x1))))) 60.02/16.10 1(0(3(4(x1)))) -> 1(2(4(0(3(x1))))) 60.02/16.10 1(0(3(4(x1)))) -> 1(2(0(4(3(x1))))) 60.02/16.10 1(0(3(4(x1)))) -> 3(1(2(0(4(x1))))) 60.02/16.10 1(0(3(4(x1)))) -> 1(2(0(3(4(x1))))) 60.02/16.10 1(0(3(4(x1)))) -> 4(3(3(1(2(0(x1)))))) 60.02/16.10 1(0(3(4(x1)))) -> 3(4(3(1(2(0(x1)))))) 60.02/16.10 1(0(3(4(x1)))) -> 3(3(1(4(2(0(x1)))))) 60.02/16.10 1(0(3(4(x1)))) -> 3(1(2(2(4(0(x1)))))) 60.02/16.10 1(0(3(4(x1)))) -> 3(1(2(5(4(0(x1)))))) 60.02/16.10 1(0(3(4(x1)))) -> 4(3(1(2(0(1(x1)))))) 60.02/16.10 1(0(3(4(x1)))) -> 3(1(4(2(0(1(x1)))))) 60.02/16.10 1(0(3(4(x1)))) -> 3(1(2(4(0(1(x1)))))) 60.02/16.10 1(0(3(4(x1)))) -> 1(2(4(0(3(1(x1)))))) 60.02/16.10 1(0(3(4(x1)))) -> 1(2(5(4(0(3(x1)))))) 60.02/16.10 1(0(3(4(x1)))) -> 1(2(4(0(1(3(x1)))))) 60.02/16.10 1(0(3(4(x1)))) -> 1(2(0(4(3(3(x1)))))) 60.02/16.10 1(0(3(4(x1)))) -> 3(1(2(0(4(3(x1)))))) 60.02/16.10 1(0(3(4(x1)))) -> 1(2(2(0(4(3(x1)))))) 60.02/16.10 1(0(3(4(x1)))) -> 1(2(5(0(4(3(x1)))))) 60.02/16.10 1(0(3(4(x1)))) -> 1(2(0(1(4(3(x1)))))) 60.02/16.10 1(0(3(4(x1)))) -> 1(2(0(3(4(3(x1)))))) 60.02/16.10 1(0(3(4(x1)))) -> 3(1(2(0(3(4(x1)))))) 60.02/16.10 1(0(3(4(x1)))) -> 1(2(5(0(3(4(x1)))))) 60.02/16.10 1(0(3(4(x1)))) -> 1(2(0(1(3(4(x1)))))) 60.02/16.10 1(0(3(4(x1)))) -> 1(2(0(3(3(4(x1)))))) 60.02/16.10 1(1(5(4(x1)))) -> 1(1(2(5(4(x1))))) 60.02/16.10 1(1(5(4(x1)))) -> 1(1(2(5(2(4(x1)))))) 60.02/16.10 1(1(5(4(x1)))) -> 1(3(1(2(5(4(x1)))))) 60.02/16.10 1(1(5(4(x1)))) -> 1(1(2(2(5(4(x1)))))) 60.02/16.10 1(1(5(4(x1)))) -> 1(1(2(5(5(4(x1)))))) 60.02/16.10 1(0(1(0(0(x1))))) -> 1(2(0(1(0(0(x1)))))) 60.02/16.10 1(1(3(0(0(x1))))) -> 0(0(1(3(1(2(x1)))))) 60.02/16.10 1(1(5(0(0(x1))))) -> 1(1(2(0(0(5(x1)))))) 60.02/16.10 1(0(1(4(0(x1))))) -> 1(0(4(0(1(2(x1)))))) 60.02/16.10 1(0(3(4(0(x1))))) -> 4(3(1(2(0(0(x1)))))) 60.02/16.10 1(0(3(4(0(x1))))) -> 1(2(0(3(4(0(x1)))))) 60.02/16.10 1(0(3(4(0(x1))))) -> 0(4(0(1(3(2(x1)))))) 60.02/16.10 1(1(3(4(0(x1))))) -> 0(3(1(4(1(2(x1)))))) 60.02/16.10 1(1(3(4(0(x1))))) -> 1(1(3(0(2(4(x1)))))) 60.02/16.10 1(1(5(4(0(x1))))) -> 1(2(5(1(0(4(x1)))))) 60.02/16.10 1(1(5(4(0(x1))))) -> 1(0(4(1(2(5(x1)))))) 60.02/16.10 1(0(3(0(4(x1))))) -> 3(1(2(4(0(0(x1)))))) 60.02/16.10 1(0(3(0(4(x1))))) -> 3(1(0(4(0(2(x1)))))) 60.02/16.10 1(0(3(0(4(x1))))) -> 1(3(0(4(0(2(x1)))))) 60.02/16.10 1(1(0(1(4(x1))))) -> 1(1(2(4(0(1(x1)))))) 60.02/16.10 1(0(1(1(4(x1))))) -> 1(1(2(0(1(4(x1)))))) 60.02/16.10 1(0(2(1(4(x1))))) -> 1(3(1(2(4(0(x1)))))) 60.02/16.10 1(0(2(1(4(x1))))) -> 3(1(4(2(0(1(x1)))))) 60.02/16.10 1(0(2(1(4(x1))))) -> 1(1(2(2(0(4(x1)))))) 60.02/16.10 1(0(2(1(4(x1))))) -> 1(2(2(0(1(4(x1)))))) 60.02/16.10 1(0(3(1(4(x1))))) -> 1(2(0(3(1(4(x1)))))) 60.02/16.10 1(0(5(1(4(x1))))) -> 2(4(0(5(1(1(x1)))))) 60.02/16.10 1(1(5(1(4(x1))))) -> 1(1(2(5(4(1(x1)))))) 60.02/16.10 1(1(0(3(4(x1))))) -> 4(1(2(0(3(1(x1)))))) 60.02/16.10 1(1(0(3(4(x1))))) -> 2(0(4(1(3(1(x1)))))) 60.02/16.10 1(1(0(3(4(x1))))) -> 0(2(4(1(3(1(x1)))))) 60.02/16.10 1(1(0(3(4(x1))))) -> 1(4(2(0(1(3(x1)))))) 60.02/16.10 1(1(0(3(4(x1))))) -> 2(0(1(1(3(4(x1)))))) 60.02/16.10 1(0(1(3(4(x1))))) -> 1(3(1(2(4(0(x1)))))) 60.02/16.10 1(0(1(3(4(x1))))) -> 1(2(0(4(3(1(x1)))))) 60.02/16.10 1(0(2(3(4(x1))))) -> 1(2(2(0(4(3(x1)))))) 60.02/16.10 1(0(2(3(4(x1))))) -> 1(2(5(0(4(3(x1)))))) 60.02/16.10 1(0(2(3(4(x1))))) -> 1(3(1(2(0(4(x1)))))) 60.02/16.10 1(0(2(3(4(x1))))) -> 3(1(2(0(3(4(x1)))))) 60.02/16.10 1(1(2(3(4(x1))))) -> 2(4(2(1(3(1(x1)))))) 60.02/16.10 1(1(2(3(4(x1))))) -> 2(5(4(1(3(1(x1)))))) 60.02/16.10 1(1(2(3(4(x1))))) -> 2(1(4(3(1(3(x1)))))) 60.02/16.10 1(1(2(3(4(x1))))) -> 2(2(1(3(1(4(x1)))))) 60.02/16.10 1(1(2(3(4(x1))))) -> 2(1(3(3(1(4(x1)))))) 60.02/16.10 1(0(3(3(4(x1))))) -> 1(2(0(3(3(4(x1)))))) 60.02/16.10 1(0(4(3(4(x1))))) -> 1(2(4(0(4(3(x1)))))) 60.02/16.10 1(0(4(3(4(x1))))) -> 3(1(2(0(4(4(x1)))))) 60.02/16.10 1(0(5(3(4(x1))))) -> 4(1(3(2(5(0(x1)))))) 60.02/16.10 1(0(5(3(4(x1))))) -> 4(5(2(0(3(1(x1)))))) 60.02/16.10 1(0(5(3(4(x1))))) -> 5(2(4(0(3(1(x1)))))) 60.02/16.10 1(0(5(3(4(x1))))) -> 2(5(0(4(3(1(x1)))))) 60.02/16.10 1(0(5(3(4(x1))))) -> 5(2(4(0(1(3(x1)))))) 60.02/16.10 1(0(5(3(4(x1))))) -> 2(4(0(5(1(3(x1)))))) 60.02/16.10 1(0(5(3(4(x1))))) -> 5(1(2(0(4(3(x1)))))) 60.02/16.10 1(0(5(3(4(x1))))) -> 2(0(5(1(4(3(x1)))))) 60.02/16.10 1(0(5(3(4(x1))))) -> 2(4(0(1(5(3(x1)))))) 60.02/16.10 1(0(5(3(4(x1))))) -> 5(1(2(0(3(4(x1)))))) 60.02/16.10 1(0(5(3(4(x1))))) -> 2(0(4(3(1(5(x1)))))) 60.02/16.10 1(1(5(3(4(x1))))) -> 3(1(2(5(4(1(x1)))))) 60.02/16.10 1(1(5(3(4(x1))))) -> 2(4(5(1(1(3(x1)))))) 60.02/16.10 1(1(5(3(4(x1))))) -> 1(2(5(4(1(3(x1)))))) 60.02/16.10 1(1(5(3(4(x1))))) -> 5(3(1(3(1(4(x1)))))) 60.02/16.10 1(1(5(3(4(x1))))) -> 3(1(2(5(1(4(x1)))))) 60.02/16.10 1(1(5(3(4(x1))))) -> 1(2(5(1(3(4(x1)))))) 60.02/16.10 1(0(1(4(4(x1))))) -> 1(2(0(1(4(4(x1)))))) 60.02/16.10 1(0(3(4(4(x1))))) -> 3(1(2(4(4(0(x1)))))) 60.02/16.10 1(0(3(4(4(x1))))) -> 4(3(1(2(0(4(x1)))))) 60.02/16.10 1(0(3(4(4(x1))))) -> 1(2(0(4(3(4(x1)))))) 60.02/16.10 1(0(3(4(4(x1))))) -> 1(2(0(3(4(4(x1)))))) 60.02/16.10 1(0(1(5(4(x1))))) -> 1(4(3(1(5(0(x1)))))) 60.02/16.10 1(0(1(5(4(x1))))) -> 1(3(1(4(5(0(x1)))))) 60.02/16.10 1(0(1(5(4(x1))))) -> 1(2(5(4(0(1(x1)))))) 60.02/16.10 1(0(1(5(4(x1))))) -> 1(1(2(5(0(4(x1)))))) 60.02/16.10 1(0(1(5(4(x1))))) -> 1(2(0(1(5(4(x1)))))) 60.02/16.10 1(0(1(5(4(x1))))) -> 1(4(2(0(1(5(x1)))))) 60.02/16.10 1(0(1(5(4(x1))))) -> 1(2(0(1(4(5(x1)))))) 60.02/16.10 1(1(1(5(4(x1))))) -> 1(1(1(2(5(4(x1)))))) 60.02/16.10 1(0(3(5(4(x1))))) -> 5(4(3(1(2(0(x1)))))) 60.02/16.10 1(0(3(5(4(x1))))) -> 4(3(1(2(5(0(x1)))))) 60.02/16.10 1(0(3(5(4(x1))))) -> 1(3(4(2(5(0(x1)))))) 60.02/16.10 1(0(3(5(4(x1))))) -> 3(1(2(4(5(0(x1)))))) 60.02/16.10 1(0(3(5(4(x1))))) -> 4(3(1(5(0(1(x1)))))) 60.02/16.10 1(0(3(5(4(x1))))) -> 4(3(3(0(5(1(x1)))))) 60.02/16.10 1(0(3(5(4(x1))))) -> 3(0(5(4(1(2(x1)))))) 60.02/16.10 1(0(3(5(4(x1))))) -> 0(5(3(1(4(2(x1)))))) 60.02/16.10 1(0(3(5(4(x1))))) -> 1(2(5(4(0(3(x1)))))) 60.02/16.10 1(0(3(5(4(x1))))) -> 2(5(1(3(0(4(x1)))))) 60.02/16.10 1(0(3(5(4(x1))))) -> 1(5(3(3(0(4(x1)))))) 60.02/16.10 1(0(3(5(4(x1))))) -> 3(1(4(5(0(4(x1)))))) 60.02/16.10 1(0(3(5(4(x1))))) -> 3(0(5(3(1(4(x1)))))) 60.02/16.10 1(0(3(5(4(x1))))) -> 0(5(5(3(1(4(x1)))))) 60.02/16.10 1(0(3(5(4(x1))))) -> 1(3(0(5(2(4(x1)))))) 60.02/16.10 1(0(3(5(4(x1))))) -> 1(3(0(2(5(4(x1)))))) 60.02/16.10 1(0(3(5(4(x1))))) -> 1(4(1(3(0(5(x1)))))) 60.02/16.10 1(0(3(5(4(x1))))) -> 1(4(4(3(0(5(x1)))))) 60.02/16.10 1(0(3(5(4(x1))))) -> 4(3(0(3(1(5(x1)))))) 60.02/16.10 1(0(3(5(4(x1))))) -> 0(4(3(1(2(5(x1)))))) 60.02/16.10 1(0(3(5(4(x1))))) -> 0(3(1(4(2(5(x1)))))) 60.02/16.10 1(0(3(5(4(x1))))) -> 1(2(4(0(3(5(x1)))))) 60.02/16.10 1(0(3(5(4(x1))))) -> 1(0(3(1(4(5(x1)))))) 60.02/16.10 1(0(3(5(4(x1))))) -> 0(2(3(1(4(5(x1)))))) 60.02/16.10 1(0(3(5(4(x1))))) -> 1(2(0(3(4(5(x1)))))) 60.02/16.10 1(1(3(5(4(x1))))) -> 5(1(3(1(4(2(x1)))))) 60.02/16.10 1(1(3(5(4(x1))))) -> 1(3(1(2(5(4(x1)))))) 60.02/16.10 1(1(3(5(4(x1))))) -> 2(1(4(3(1(5(x1)))))) 60.02/16.10 1(1(3(5(4(x1))))) -> 3(1(4(1(2(5(x1)))))) 60.02/16.10 1(1(3(5(4(x1))))) -> 1(3(1(2(4(5(x1)))))) 60.02/16.10 1(1(5(5(4(x1))))) -> 4(1(1(2(5(5(x1)))))) 60.02/16.10 1(1(5(5(4(x1))))) -> 1(1(4(2(5(5(x1)))))) 60.02/16.10 60.02/16.10 Q is empty. 60.02/16.10 We have to consider all minimal (P,Q,R)-chains. 60.02/16.10 ---------------------------------------- 60.02/16.10 60.02/16.10 (9) UsableRulesProof (EQUIVALENT) 60.02/16.10 We can use the usable rules and reduction pair processor [LPAR04] with the Ce-compatible extension of the polynomial order that maps every function symbol to the sum of its arguments. Then, we can delete all non-usable rules [FROCOS05] from R. 60.02/16.10 ---------------------------------------- 60.02/16.10 60.02/16.10 (10) 60.02/16.10 Obligation: 60.02/16.10 Q DP problem: 60.02/16.10 The TRS P consists of the following rules: 60.02/16.10 60.02/16.10 1^1(1(5(1(4(x1))))) -> 1^1(x1) 60.02/16.10 1^1(1(2(3(4(x1))))) -> 1^1(x1) 60.02/16.10 1^1(1(5(3(4(x1))))) -> 1^1(x1) 60.02/16.10 60.02/16.10 R is empty. 60.02/16.10 Q is empty. 60.02/16.10 We have to consider all minimal (P,Q,R)-chains. 60.02/16.10 ---------------------------------------- 60.02/16.10 60.02/16.10 (11) QDPSizeChangeProof (EQUIVALENT) 60.02/16.10 By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 60.02/16.10 60.02/16.10 From the DPs we obtained the following set of size-change graphs: 60.02/16.10 *1^1(1(5(1(4(x1))))) -> 1^1(x1) 60.02/16.10 The graph contains the following edges 1 > 1 60.02/16.10 60.02/16.10 60.02/16.10 *1^1(1(2(3(4(x1))))) -> 1^1(x1) 60.02/16.10 The graph contains the following edges 1 > 1 60.02/16.10 60.02/16.10 60.02/16.10 *1^1(1(5(3(4(x1))))) -> 1^1(x1) 60.02/16.10 The graph contains the following edges 1 > 1 60.02/16.10 60.02/16.10 60.02/16.10 ---------------------------------------- 60.02/16.10 60.02/16.10 (12) 60.02/16.10 YES 60.25/16.18 EOF