33.00/9.18 YES 33.00/9.20 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 33.00/9.20 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 33.00/9.20 33.00/9.20 33.00/9.20 Termination w.r.t. Q of the given QTRS could be proven: 33.00/9.20 33.00/9.20 (0) QTRS 33.00/9.20 (1) DependencyPairsProof [EQUIVALENT, 206 ms] 33.00/9.20 (2) QDP 33.00/9.20 (3) DependencyGraphProof [EQUIVALENT, 0 ms] 33.00/9.20 (4) AND 33.00/9.20 (5) QDP 33.00/9.20 (6) UsableRulesProof [EQUIVALENT, 0 ms] 33.00/9.20 (7) QDP 33.00/9.20 (8) DependencyGraphProof [EQUIVALENT, 0 ms] 33.00/9.20 (9) QDP 33.00/9.20 (10) QDPOrderProof [EQUIVALENT, 70 ms] 33.00/9.20 (11) QDP 33.00/9.20 (12) PisEmptyProof [EQUIVALENT, 0 ms] 33.00/9.20 (13) YES 33.00/9.20 (14) QDP 33.00/9.20 (15) UsableRulesProof [EQUIVALENT, 0 ms] 33.00/9.20 (16) QDP 33.00/9.20 (17) QDPOrderProof [EQUIVALENT, 40 ms] 33.00/9.20 (18) QDP 33.00/9.20 (19) PisEmptyProof [EQUIVALENT, 0 ms] 33.00/9.20 (20) YES 33.00/9.20 33.00/9.20 33.00/9.20 ---------------------------------------- 33.00/9.20 33.00/9.20 (0) 33.00/9.20 Obligation: 33.00/9.20 Q restricted rewrite system: 33.00/9.20 The TRS R consists of the following rules: 33.00/9.20 33.00/9.20 0(1(1(x1))) -> 1(0(2(1(x1)))) 33.00/9.20 0(1(1(x1))) -> 1(1(0(3(2(x1))))) 33.00/9.20 0(1(1(x1))) -> 1(4(0(0(2(1(x1)))))) 33.00/9.20 0(1(4(x1))) -> 1(4(0(3(x1)))) 33.00/9.20 0(1(4(x1))) -> 4(0(2(1(x1)))) 33.00/9.20 0(1(4(x1))) -> 4(0(2(1(3(x1))))) 33.00/9.20 0(4(1(x1))) -> 0(2(4(1(x1)))) 33.00/9.20 0(4(1(x1))) -> 4(0(2(1(x1)))) 33.00/9.20 0(4(1(x1))) -> 4(0(3(1(x1)))) 33.00/9.20 0(4(1(x1))) -> 1(4(4(0(2(x1))))) 33.00/9.20 0(4(1(x1))) -> 2(1(4(0(2(x1))))) 33.00/9.20 0(5(4(x1))) -> 1(4(0(0(2(5(x1)))))) 33.00/9.20 0(5(4(x1))) -> 4(0(2(5(2(5(x1)))))) 33.00/9.20 0(5(4(x1))) -> 5(0(4(0(3(3(x1)))))) 33.00/9.20 4(2(1(x1))) -> 4(0(2(1(x1)))) 33.00/9.20 4(2(1(x1))) -> 1(2(4(0(2(x1))))) 33.00/9.20 0(1(0(4(x1)))) -> 0(0(2(2(1(4(x1)))))) 33.00/9.20 0(1(1(2(x1)))) -> 5(1(0(2(1(x1))))) 33.00/9.20 0(1(1(3(x1)))) -> 1(1(5(0(3(x1))))) 33.00/9.20 0(1(4(1(x1)))) -> 1(0(2(4(1(x1))))) 33.00/9.20 0(1(4(3(x1)))) -> 1(0(2(4(3(x1))))) 33.00/9.20 0(1(4(3(x1)))) -> 4(0(2(1(3(x1))))) 33.00/9.20 0(4(1(2(x1)))) -> 2(0(3(1(4(x1))))) 33.00/9.20 0(4(2(1(x1)))) -> 0(4(3(0(2(1(x1)))))) 33.00/9.20 0(5(0(4(x1)))) -> 1(5(4(0(0(2(x1)))))) 33.00/9.20 0(5(1(3(x1)))) -> 1(1(5(0(3(x1))))) 33.00/9.20 0(5(1(3(x1)))) -> 5(3(1(0(3(x1))))) 33.00/9.20 0(5(4(1(x1)))) -> 4(1(5(4(0(2(x1)))))) 33.00/9.20 0(5(4(3(x1)))) -> 0(2(5(0(3(4(x1)))))) 33.00/9.20 0(5(4(3(x1)))) -> 1(5(3(4(0(3(x1)))))) 33.00/9.20 1(0(5(4(x1)))) -> 1(4(5(0(3(3(x1)))))) 33.00/9.20 1(0(5(4(x1)))) -> 5(5(1(0(2(4(x1)))))) 33.00/9.20 1(4(2(1(x1)))) -> 4(0(2(1(2(1(x1)))))) 33.00/9.20 4(1(2(1(x1)))) -> 4(1(0(2(1(x1))))) 33.00/9.20 4(1(2(1(x1)))) -> 3(4(0(2(1(1(x1)))))) 33.00/9.20 4(3(2(1(x1)))) -> 0(3(4(0(2(1(x1)))))) 33.00/9.20 0(0(1(2(3(x1))))) -> 1(0(3(0(0(2(x1)))))) 33.00/9.20 0(0(5(1(2(x1))))) -> 0(0(2(5(0(1(x1)))))) 33.00/9.20 0(0(5(1(3(x1))))) -> 4(5(0(0(3(1(x1)))))) 33.00/9.20 0(1(3(4(2(x1))))) -> 1(3(4(3(0(2(x1)))))) 33.00/9.20 0(4(5(3(4(x1))))) -> 0(3(2(5(4(4(x1)))))) 33.00/9.20 0(5(0(2(2(x1))))) -> 0(0(2(5(2(4(x1)))))) 33.00/9.20 0(5(1(1(3(x1))))) -> 0(3(2(1(1(5(x1)))))) 33.00/9.20 0(5(1(4(3(x1))))) -> 3(0(2(1(5(4(x1)))))) 33.00/9.20 0(5(5(1(2(x1))))) -> 1(5(3(0(2(5(x1)))))) 33.00/9.20 1(0(1(2(4(x1))))) -> 1(1(0(2(3(4(x1)))))) 33.00/9.20 1(4(2(1(2(x1))))) -> 0(2(2(1(1(4(x1)))))) 33.00/9.20 4(0(0(5(4(x1))))) -> 5(0(0(4(4(5(x1)))))) 33.00/9.20 4(2(5(4(1(x1))))) -> 4(4(1(5(3(2(x1)))))) 33.00/9.20 33.00/9.20 Q is empty. 33.00/9.20 33.00/9.20 ---------------------------------------- 33.00/9.20 33.00/9.20 (1) DependencyPairsProof (EQUIVALENT) 33.00/9.20 Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. 33.00/9.20 ---------------------------------------- 33.00/9.20 33.00/9.20 (2) 33.00/9.20 Obligation: 33.00/9.20 Q DP problem: 33.00/9.20 The TRS P consists of the following rules: 33.00/9.20 33.00/9.20 0^1(1(1(x1))) -> 1^1(0(2(1(x1)))) 33.00/9.20 0^1(1(1(x1))) -> 0^1(2(1(x1))) 33.00/9.20 0^1(1(1(x1))) -> 1^1(1(0(3(2(x1))))) 33.00/9.20 0^1(1(1(x1))) -> 1^1(0(3(2(x1)))) 33.00/9.20 0^1(1(1(x1))) -> 0^1(3(2(x1))) 33.00/9.20 0^1(1(1(x1))) -> 1^1(4(0(0(2(1(x1)))))) 33.00/9.20 0^1(1(1(x1))) -> 4^1(0(0(2(1(x1))))) 33.00/9.20 0^1(1(1(x1))) -> 0^1(0(2(1(x1)))) 33.00/9.20 0^1(1(4(x1))) -> 1^1(4(0(3(x1)))) 33.00/9.20 0^1(1(4(x1))) -> 4^1(0(3(x1))) 33.00/9.20 0^1(1(4(x1))) -> 0^1(3(x1)) 33.00/9.20 0^1(1(4(x1))) -> 4^1(0(2(1(x1)))) 33.00/9.20 0^1(1(4(x1))) -> 0^1(2(1(x1))) 33.00/9.20 0^1(1(4(x1))) -> 1^1(x1) 33.00/9.20 0^1(1(4(x1))) -> 4^1(0(2(1(3(x1))))) 33.00/9.20 0^1(1(4(x1))) -> 0^1(2(1(3(x1)))) 33.00/9.20 0^1(1(4(x1))) -> 1^1(3(x1)) 33.00/9.20 0^1(4(1(x1))) -> 0^1(2(4(1(x1)))) 33.00/9.20 0^1(4(1(x1))) -> 4^1(0(2(1(x1)))) 33.00/9.20 0^1(4(1(x1))) -> 0^1(2(1(x1))) 33.00/9.20 0^1(4(1(x1))) -> 4^1(0(3(1(x1)))) 33.00/9.20 0^1(4(1(x1))) -> 0^1(3(1(x1))) 33.00/9.20 0^1(4(1(x1))) -> 1^1(4(4(0(2(x1))))) 33.00/9.20 0^1(4(1(x1))) -> 4^1(4(0(2(x1)))) 33.00/9.20 0^1(4(1(x1))) -> 4^1(0(2(x1))) 33.00/9.20 0^1(4(1(x1))) -> 0^1(2(x1)) 33.00/9.20 0^1(4(1(x1))) -> 1^1(4(0(2(x1)))) 33.00/9.20 0^1(5(4(x1))) -> 1^1(4(0(0(2(5(x1)))))) 33.00/9.20 0^1(5(4(x1))) -> 4^1(0(0(2(5(x1))))) 33.00/9.20 0^1(5(4(x1))) -> 0^1(0(2(5(x1)))) 33.00/9.20 0^1(5(4(x1))) -> 0^1(2(5(x1))) 33.00/9.20 0^1(5(4(x1))) -> 4^1(0(2(5(2(5(x1)))))) 33.00/9.20 0^1(5(4(x1))) -> 0^1(2(5(2(5(x1))))) 33.00/9.20 0^1(5(4(x1))) -> 0^1(4(0(3(3(x1))))) 33.00/9.20 0^1(5(4(x1))) -> 4^1(0(3(3(x1)))) 33.00/9.20 0^1(5(4(x1))) -> 0^1(3(3(x1))) 33.00/9.20 4^1(2(1(x1))) -> 4^1(0(2(1(x1)))) 33.00/9.20 4^1(2(1(x1))) -> 0^1(2(1(x1))) 33.00/9.20 4^1(2(1(x1))) -> 1^1(2(4(0(2(x1))))) 33.00/9.20 4^1(2(1(x1))) -> 4^1(0(2(x1))) 33.00/9.20 4^1(2(1(x1))) -> 0^1(2(x1)) 33.00/9.20 0^1(1(0(4(x1)))) -> 0^1(0(2(2(1(4(x1)))))) 33.00/9.20 0^1(1(0(4(x1)))) -> 0^1(2(2(1(4(x1))))) 33.00/9.20 0^1(1(0(4(x1)))) -> 1^1(4(x1)) 33.00/9.20 0^1(1(1(2(x1)))) -> 1^1(0(2(1(x1)))) 33.00/9.20 0^1(1(1(2(x1)))) -> 0^1(2(1(x1))) 33.00/9.20 0^1(1(1(2(x1)))) -> 1^1(x1) 33.00/9.20 0^1(1(1(3(x1)))) -> 1^1(1(5(0(3(x1))))) 33.00/9.20 0^1(1(1(3(x1)))) -> 1^1(5(0(3(x1)))) 33.00/9.20 0^1(1(1(3(x1)))) -> 0^1(3(x1)) 33.00/9.20 0^1(1(4(1(x1)))) -> 1^1(0(2(4(1(x1))))) 33.00/9.20 0^1(1(4(1(x1)))) -> 0^1(2(4(1(x1)))) 33.00/9.20 0^1(1(4(3(x1)))) -> 1^1(0(2(4(3(x1))))) 33.00/9.20 0^1(1(4(3(x1)))) -> 0^1(2(4(3(x1)))) 33.00/9.20 0^1(1(4(3(x1)))) -> 4^1(0(2(1(3(x1))))) 33.00/9.20 0^1(1(4(3(x1)))) -> 0^1(2(1(3(x1)))) 33.00/9.20 0^1(1(4(3(x1)))) -> 1^1(3(x1)) 33.00/9.20 0^1(4(1(2(x1)))) -> 0^1(3(1(4(x1)))) 33.00/9.20 0^1(4(1(2(x1)))) -> 1^1(4(x1)) 33.00/9.20 0^1(4(1(2(x1)))) -> 4^1(x1) 33.00/9.20 0^1(4(2(1(x1)))) -> 0^1(4(3(0(2(1(x1)))))) 33.00/9.20 0^1(4(2(1(x1)))) -> 4^1(3(0(2(1(x1))))) 33.00/9.20 0^1(4(2(1(x1)))) -> 0^1(2(1(x1))) 33.00/9.20 0^1(5(0(4(x1)))) -> 1^1(5(4(0(0(2(x1)))))) 33.00/9.20 0^1(5(0(4(x1)))) -> 4^1(0(0(2(x1)))) 33.00/9.20 0^1(5(0(4(x1)))) -> 0^1(0(2(x1))) 33.00/9.20 0^1(5(0(4(x1)))) -> 0^1(2(x1)) 33.00/9.20 0^1(5(1(3(x1)))) -> 1^1(1(5(0(3(x1))))) 33.00/9.20 0^1(5(1(3(x1)))) -> 1^1(5(0(3(x1)))) 33.00/9.20 0^1(5(1(3(x1)))) -> 0^1(3(x1)) 33.00/9.20 0^1(5(1(3(x1)))) -> 1^1(0(3(x1))) 33.00/9.20 0^1(5(4(1(x1)))) -> 4^1(1(5(4(0(2(x1)))))) 33.00/9.20 0^1(5(4(1(x1)))) -> 1^1(5(4(0(2(x1))))) 33.00/9.20 0^1(5(4(1(x1)))) -> 4^1(0(2(x1))) 33.00/9.20 0^1(5(4(1(x1)))) -> 0^1(2(x1)) 33.00/9.20 0^1(5(4(3(x1)))) -> 0^1(2(5(0(3(4(x1)))))) 33.00/9.20 0^1(5(4(3(x1)))) -> 0^1(3(4(x1))) 33.00/9.20 0^1(5(4(3(x1)))) -> 4^1(x1) 33.00/9.20 0^1(5(4(3(x1)))) -> 1^1(5(3(4(0(3(x1)))))) 33.00/9.20 0^1(5(4(3(x1)))) -> 4^1(0(3(x1))) 33.00/9.20 0^1(5(4(3(x1)))) -> 0^1(3(x1)) 33.00/9.20 1^1(0(5(4(x1)))) -> 1^1(4(5(0(3(3(x1)))))) 33.00/9.20 1^1(0(5(4(x1)))) -> 4^1(5(0(3(3(x1))))) 33.00/9.20 1^1(0(5(4(x1)))) -> 0^1(3(3(x1))) 33.00/9.20 1^1(0(5(4(x1)))) -> 1^1(0(2(4(x1)))) 33.00/9.20 1^1(0(5(4(x1)))) -> 0^1(2(4(x1))) 33.00/9.20 1^1(4(2(1(x1)))) -> 4^1(0(2(1(2(1(x1)))))) 33.00/9.20 1^1(4(2(1(x1)))) -> 0^1(2(1(2(1(x1))))) 33.00/9.20 1^1(4(2(1(x1)))) -> 1^1(2(1(x1))) 33.00/9.20 4^1(1(2(1(x1)))) -> 4^1(1(0(2(1(x1))))) 33.00/9.20 4^1(1(2(1(x1)))) -> 1^1(0(2(1(x1)))) 33.00/9.20 4^1(1(2(1(x1)))) -> 0^1(2(1(x1))) 33.00/9.20 4^1(1(2(1(x1)))) -> 4^1(0(2(1(1(x1))))) 33.00/9.20 4^1(1(2(1(x1)))) -> 0^1(2(1(1(x1)))) 33.00/9.20 4^1(1(2(1(x1)))) -> 1^1(1(x1)) 33.00/9.20 4^1(3(2(1(x1)))) -> 0^1(3(4(0(2(1(x1)))))) 33.00/9.20 4^1(3(2(1(x1)))) -> 4^1(0(2(1(x1)))) 33.00/9.20 4^1(3(2(1(x1)))) -> 0^1(2(1(x1))) 33.00/9.20 0^1(0(1(2(3(x1))))) -> 1^1(0(3(0(0(2(x1)))))) 33.00/9.20 0^1(0(1(2(3(x1))))) -> 0^1(3(0(0(2(x1))))) 33.00/9.20 0^1(0(1(2(3(x1))))) -> 0^1(0(2(x1))) 33.00/9.20 0^1(0(1(2(3(x1))))) -> 0^1(2(x1)) 33.00/9.20 0^1(0(5(1(2(x1))))) -> 0^1(0(2(5(0(1(x1)))))) 33.00/9.20 0^1(0(5(1(2(x1))))) -> 0^1(2(5(0(1(x1))))) 33.00/9.20 0^1(0(5(1(2(x1))))) -> 0^1(1(x1)) 33.00/9.20 0^1(0(5(1(2(x1))))) -> 1^1(x1) 33.00/9.20 0^1(0(5(1(3(x1))))) -> 4^1(5(0(0(3(1(x1)))))) 33.00/9.20 0^1(0(5(1(3(x1))))) -> 0^1(0(3(1(x1)))) 33.00/9.20 0^1(0(5(1(3(x1))))) -> 0^1(3(1(x1))) 33.00/9.20 0^1(0(5(1(3(x1))))) -> 1^1(x1) 33.00/9.20 0^1(1(3(4(2(x1))))) -> 1^1(3(4(3(0(2(x1)))))) 33.00/9.20 0^1(1(3(4(2(x1))))) -> 4^1(3(0(2(x1)))) 33.00/9.20 0^1(1(3(4(2(x1))))) -> 0^1(2(x1)) 33.00/9.20 0^1(4(5(3(4(x1))))) -> 0^1(3(2(5(4(4(x1)))))) 33.00/9.20 0^1(4(5(3(4(x1))))) -> 4^1(4(x1)) 33.00/9.20 0^1(5(0(2(2(x1))))) -> 0^1(0(2(5(2(4(x1)))))) 33.00/9.20 0^1(5(0(2(2(x1))))) -> 0^1(2(5(2(4(x1))))) 33.00/9.20 0^1(5(0(2(2(x1))))) -> 4^1(x1) 33.00/9.20 0^1(5(1(1(3(x1))))) -> 0^1(3(2(1(1(5(x1)))))) 33.00/9.20 0^1(5(1(1(3(x1))))) -> 1^1(1(5(x1))) 33.00/9.20 0^1(5(1(1(3(x1))))) -> 1^1(5(x1)) 33.00/9.20 0^1(5(1(4(3(x1))))) -> 0^1(2(1(5(4(x1))))) 33.00/9.20 0^1(5(1(4(3(x1))))) -> 1^1(5(4(x1))) 33.00/9.20 0^1(5(1(4(3(x1))))) -> 4^1(x1) 33.00/9.20 0^1(5(5(1(2(x1))))) -> 1^1(5(3(0(2(5(x1)))))) 33.00/9.20 0^1(5(5(1(2(x1))))) -> 0^1(2(5(x1))) 33.00/9.20 1^1(0(1(2(4(x1))))) -> 1^1(1(0(2(3(4(x1)))))) 33.00/9.20 1^1(0(1(2(4(x1))))) -> 1^1(0(2(3(4(x1))))) 33.00/9.21 1^1(0(1(2(4(x1))))) -> 0^1(2(3(4(x1)))) 33.00/9.21 1^1(4(2(1(2(x1))))) -> 0^1(2(2(1(1(4(x1)))))) 33.00/9.21 1^1(4(2(1(2(x1))))) -> 1^1(1(4(x1))) 33.00/9.21 1^1(4(2(1(2(x1))))) -> 1^1(4(x1)) 33.00/9.21 1^1(4(2(1(2(x1))))) -> 4^1(x1) 33.00/9.21 4^1(0(0(5(4(x1))))) -> 0^1(0(4(4(5(x1))))) 33.00/9.21 4^1(0(0(5(4(x1))))) -> 0^1(4(4(5(x1)))) 33.00/9.21 4^1(0(0(5(4(x1))))) -> 4^1(4(5(x1))) 33.00/9.21 4^1(0(0(5(4(x1))))) -> 4^1(5(x1)) 33.00/9.21 4^1(2(5(4(1(x1))))) -> 4^1(4(1(5(3(2(x1)))))) 33.00/9.21 4^1(2(5(4(1(x1))))) -> 4^1(1(5(3(2(x1))))) 33.00/9.21 4^1(2(5(4(1(x1))))) -> 1^1(5(3(2(x1)))) 33.00/9.21 33.00/9.21 The TRS R consists of the following rules: 33.00/9.21 33.00/9.21 0(1(1(x1))) -> 1(0(2(1(x1)))) 33.00/9.21 0(1(1(x1))) -> 1(1(0(3(2(x1))))) 33.00/9.21 0(1(1(x1))) -> 1(4(0(0(2(1(x1)))))) 33.00/9.21 0(1(4(x1))) -> 1(4(0(3(x1)))) 33.00/9.21 0(1(4(x1))) -> 4(0(2(1(x1)))) 33.00/9.21 0(1(4(x1))) -> 4(0(2(1(3(x1))))) 33.00/9.21 0(4(1(x1))) -> 0(2(4(1(x1)))) 33.00/9.21 0(4(1(x1))) -> 4(0(2(1(x1)))) 33.00/9.21 0(4(1(x1))) -> 4(0(3(1(x1)))) 33.00/9.21 0(4(1(x1))) -> 1(4(4(0(2(x1))))) 33.00/9.21 0(4(1(x1))) -> 2(1(4(0(2(x1))))) 33.00/9.21 0(5(4(x1))) -> 1(4(0(0(2(5(x1)))))) 33.00/9.21 0(5(4(x1))) -> 4(0(2(5(2(5(x1)))))) 33.00/9.21 0(5(4(x1))) -> 5(0(4(0(3(3(x1)))))) 33.00/9.21 4(2(1(x1))) -> 4(0(2(1(x1)))) 33.00/9.21 4(2(1(x1))) -> 1(2(4(0(2(x1))))) 33.00/9.21 0(1(0(4(x1)))) -> 0(0(2(2(1(4(x1)))))) 33.00/9.21 0(1(1(2(x1)))) -> 5(1(0(2(1(x1))))) 33.00/9.21 0(1(1(3(x1)))) -> 1(1(5(0(3(x1))))) 33.00/9.21 0(1(4(1(x1)))) -> 1(0(2(4(1(x1))))) 33.00/9.21 0(1(4(3(x1)))) -> 1(0(2(4(3(x1))))) 33.00/9.21 0(1(4(3(x1)))) -> 4(0(2(1(3(x1))))) 33.00/9.21 0(4(1(2(x1)))) -> 2(0(3(1(4(x1))))) 33.00/9.21 0(4(2(1(x1)))) -> 0(4(3(0(2(1(x1)))))) 33.00/9.21 0(5(0(4(x1)))) -> 1(5(4(0(0(2(x1)))))) 33.00/9.21 0(5(1(3(x1)))) -> 1(1(5(0(3(x1))))) 33.00/9.21 0(5(1(3(x1)))) -> 5(3(1(0(3(x1))))) 33.00/9.21 0(5(4(1(x1)))) -> 4(1(5(4(0(2(x1)))))) 33.00/9.21 0(5(4(3(x1)))) -> 0(2(5(0(3(4(x1)))))) 33.00/9.21 0(5(4(3(x1)))) -> 1(5(3(4(0(3(x1)))))) 33.00/9.21 1(0(5(4(x1)))) -> 1(4(5(0(3(3(x1)))))) 33.00/9.21 1(0(5(4(x1)))) -> 5(5(1(0(2(4(x1)))))) 33.00/9.21 1(4(2(1(x1)))) -> 4(0(2(1(2(1(x1)))))) 33.00/9.21 4(1(2(1(x1)))) -> 4(1(0(2(1(x1))))) 33.00/9.21 4(1(2(1(x1)))) -> 3(4(0(2(1(1(x1)))))) 33.00/9.21 4(3(2(1(x1)))) -> 0(3(4(0(2(1(x1)))))) 33.00/9.21 0(0(1(2(3(x1))))) -> 1(0(3(0(0(2(x1)))))) 33.00/9.21 0(0(5(1(2(x1))))) -> 0(0(2(5(0(1(x1)))))) 33.00/9.21 0(0(5(1(3(x1))))) -> 4(5(0(0(3(1(x1)))))) 33.00/9.21 0(1(3(4(2(x1))))) -> 1(3(4(3(0(2(x1)))))) 33.00/9.21 0(4(5(3(4(x1))))) -> 0(3(2(5(4(4(x1)))))) 33.00/9.21 0(5(0(2(2(x1))))) -> 0(0(2(5(2(4(x1)))))) 33.00/9.21 0(5(1(1(3(x1))))) -> 0(3(2(1(1(5(x1)))))) 33.00/9.21 0(5(1(4(3(x1))))) -> 3(0(2(1(5(4(x1)))))) 33.00/9.21 0(5(5(1(2(x1))))) -> 1(5(3(0(2(5(x1)))))) 33.00/9.21 1(0(1(2(4(x1))))) -> 1(1(0(2(3(4(x1)))))) 33.00/9.21 1(4(2(1(2(x1))))) -> 0(2(2(1(1(4(x1)))))) 33.00/9.21 4(0(0(5(4(x1))))) -> 5(0(0(4(4(5(x1)))))) 33.00/9.21 4(2(5(4(1(x1))))) -> 4(4(1(5(3(2(x1)))))) 33.00/9.21 33.00/9.21 Q is empty. 33.00/9.21 We have to consider all minimal (P,Q,R)-chains. 33.00/9.21 ---------------------------------------- 33.00/9.21 33.00/9.21 (3) DependencyGraphProof (EQUIVALENT) 33.00/9.21 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 2 SCCs with 135 less nodes. 33.00/9.21 ---------------------------------------- 33.00/9.21 33.00/9.21 (4) 33.00/9.21 Complex Obligation (AND) 33.00/9.21 33.00/9.21 ---------------------------------------- 33.00/9.21 33.00/9.21 (5) 33.00/9.21 Obligation: 33.00/9.21 Q DP problem: 33.00/9.21 The TRS P consists of the following rules: 33.00/9.21 33.00/9.21 4^1(1(2(1(x1)))) -> 1^1(1(x1)) 33.00/9.21 1^1(4(2(1(2(x1))))) -> 1^1(1(4(x1))) 33.00/9.21 1^1(4(2(1(2(x1))))) -> 1^1(4(x1)) 33.00/9.21 1^1(4(2(1(2(x1))))) -> 4^1(x1) 33.00/9.21 33.00/9.21 The TRS R consists of the following rules: 33.00/9.21 33.00/9.21 0(1(1(x1))) -> 1(0(2(1(x1)))) 33.00/9.21 0(1(1(x1))) -> 1(1(0(3(2(x1))))) 33.00/9.21 0(1(1(x1))) -> 1(4(0(0(2(1(x1)))))) 33.00/9.21 0(1(4(x1))) -> 1(4(0(3(x1)))) 33.00/9.21 0(1(4(x1))) -> 4(0(2(1(x1)))) 33.00/9.21 0(1(4(x1))) -> 4(0(2(1(3(x1))))) 33.00/9.21 0(4(1(x1))) -> 0(2(4(1(x1)))) 33.00/9.21 0(4(1(x1))) -> 4(0(2(1(x1)))) 33.00/9.21 0(4(1(x1))) -> 4(0(3(1(x1)))) 33.00/9.21 0(4(1(x1))) -> 1(4(4(0(2(x1))))) 33.00/9.21 0(4(1(x1))) -> 2(1(4(0(2(x1))))) 33.00/9.21 0(5(4(x1))) -> 1(4(0(0(2(5(x1)))))) 33.00/9.21 0(5(4(x1))) -> 4(0(2(5(2(5(x1)))))) 33.00/9.21 0(5(4(x1))) -> 5(0(4(0(3(3(x1)))))) 33.00/9.21 4(2(1(x1))) -> 4(0(2(1(x1)))) 33.00/9.21 4(2(1(x1))) -> 1(2(4(0(2(x1))))) 33.00/9.21 0(1(0(4(x1)))) -> 0(0(2(2(1(4(x1)))))) 33.00/9.21 0(1(1(2(x1)))) -> 5(1(0(2(1(x1))))) 33.00/9.21 0(1(1(3(x1)))) -> 1(1(5(0(3(x1))))) 33.00/9.21 0(1(4(1(x1)))) -> 1(0(2(4(1(x1))))) 33.00/9.21 0(1(4(3(x1)))) -> 1(0(2(4(3(x1))))) 33.00/9.21 0(1(4(3(x1)))) -> 4(0(2(1(3(x1))))) 33.00/9.21 0(4(1(2(x1)))) -> 2(0(3(1(4(x1))))) 33.00/9.21 0(4(2(1(x1)))) -> 0(4(3(0(2(1(x1)))))) 33.00/9.21 0(5(0(4(x1)))) -> 1(5(4(0(0(2(x1)))))) 33.00/9.21 0(5(1(3(x1)))) -> 1(1(5(0(3(x1))))) 33.00/9.21 0(5(1(3(x1)))) -> 5(3(1(0(3(x1))))) 33.00/9.21 0(5(4(1(x1)))) -> 4(1(5(4(0(2(x1)))))) 33.00/9.21 0(5(4(3(x1)))) -> 0(2(5(0(3(4(x1)))))) 33.00/9.21 0(5(4(3(x1)))) -> 1(5(3(4(0(3(x1)))))) 33.00/9.21 1(0(5(4(x1)))) -> 1(4(5(0(3(3(x1)))))) 33.00/9.21 1(0(5(4(x1)))) -> 5(5(1(0(2(4(x1)))))) 33.00/9.21 1(4(2(1(x1)))) -> 4(0(2(1(2(1(x1)))))) 33.00/9.21 4(1(2(1(x1)))) -> 4(1(0(2(1(x1))))) 33.00/9.21 4(1(2(1(x1)))) -> 3(4(0(2(1(1(x1)))))) 33.00/9.21 4(3(2(1(x1)))) -> 0(3(4(0(2(1(x1)))))) 33.00/9.21 0(0(1(2(3(x1))))) -> 1(0(3(0(0(2(x1)))))) 33.00/9.21 0(0(5(1(2(x1))))) -> 0(0(2(5(0(1(x1)))))) 33.00/9.21 0(0(5(1(3(x1))))) -> 4(5(0(0(3(1(x1)))))) 33.00/9.21 0(1(3(4(2(x1))))) -> 1(3(4(3(0(2(x1)))))) 33.00/9.21 0(4(5(3(4(x1))))) -> 0(3(2(5(4(4(x1)))))) 33.00/9.21 0(5(0(2(2(x1))))) -> 0(0(2(5(2(4(x1)))))) 33.00/9.21 0(5(1(1(3(x1))))) -> 0(3(2(1(1(5(x1)))))) 33.00/9.21 0(5(1(4(3(x1))))) -> 3(0(2(1(5(4(x1)))))) 33.00/9.21 0(5(5(1(2(x1))))) -> 1(5(3(0(2(5(x1)))))) 33.00/9.21 1(0(1(2(4(x1))))) -> 1(1(0(2(3(4(x1)))))) 33.00/9.21 1(4(2(1(2(x1))))) -> 0(2(2(1(1(4(x1)))))) 33.00/9.21 4(0(0(5(4(x1))))) -> 5(0(0(4(4(5(x1)))))) 33.00/9.21 4(2(5(4(1(x1))))) -> 4(4(1(5(3(2(x1)))))) 33.00/9.21 33.00/9.21 Q is empty. 33.00/9.21 We have to consider all minimal (P,Q,R)-chains. 33.00/9.21 ---------------------------------------- 33.00/9.21 33.00/9.21 (6) UsableRulesProof (EQUIVALENT) 33.00/9.21 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. 33.00/9.21 ---------------------------------------- 33.00/9.21 33.00/9.21 (7) 33.00/9.21 Obligation: 33.00/9.21 Q DP problem: 33.00/9.21 The TRS P consists of the following rules: 33.00/9.21 33.00/9.21 4^1(1(2(1(x1)))) -> 1^1(1(x1)) 33.00/9.21 1^1(4(2(1(2(x1))))) -> 1^1(1(4(x1))) 33.00/9.21 1^1(4(2(1(2(x1))))) -> 1^1(4(x1)) 33.00/9.21 1^1(4(2(1(2(x1))))) -> 4^1(x1) 33.00/9.21 33.00/9.21 The TRS R consists of the following rules: 33.00/9.21 33.00/9.21 4(2(1(x1))) -> 4(0(2(1(x1)))) 33.00/9.21 4(2(1(x1))) -> 1(2(4(0(2(x1))))) 33.00/9.21 4(1(2(1(x1)))) -> 4(1(0(2(1(x1))))) 33.00/9.21 4(1(2(1(x1)))) -> 3(4(0(2(1(1(x1)))))) 33.00/9.21 4(3(2(1(x1)))) -> 0(3(4(0(2(1(x1)))))) 33.00/9.21 4(0(0(5(4(x1))))) -> 5(0(0(4(4(5(x1)))))) 33.00/9.21 4(2(5(4(1(x1))))) -> 4(4(1(5(3(2(x1)))))) 33.00/9.21 1(0(5(4(x1)))) -> 1(4(5(0(3(3(x1)))))) 33.00/9.21 1(0(5(4(x1)))) -> 5(5(1(0(2(4(x1)))))) 33.00/9.21 1(4(2(1(x1)))) -> 4(0(2(1(2(1(x1)))))) 33.00/9.21 1(0(1(2(4(x1))))) -> 1(1(0(2(3(4(x1)))))) 33.00/9.21 1(4(2(1(2(x1))))) -> 0(2(2(1(1(4(x1)))))) 33.00/9.21 33.00/9.21 Q is empty. 33.00/9.21 We have to consider all minimal (P,Q,R)-chains. 33.00/9.21 ---------------------------------------- 33.00/9.21 33.00/9.21 (8) DependencyGraphProof (EQUIVALENT) 33.00/9.21 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 3 less nodes. 33.00/9.21 ---------------------------------------- 33.00/9.21 33.00/9.21 (9) 33.00/9.21 Obligation: 33.00/9.21 Q DP problem: 33.00/9.21 The TRS P consists of the following rules: 33.00/9.21 33.00/9.21 1^1(4(2(1(2(x1))))) -> 1^1(4(x1)) 33.00/9.21 33.00/9.21 The TRS R consists of the following rules: 33.00/9.21 33.00/9.21 4(2(1(x1))) -> 4(0(2(1(x1)))) 33.00/9.21 4(2(1(x1))) -> 1(2(4(0(2(x1))))) 33.00/9.21 4(1(2(1(x1)))) -> 4(1(0(2(1(x1))))) 33.00/9.21 4(1(2(1(x1)))) -> 3(4(0(2(1(1(x1)))))) 33.00/9.21 4(3(2(1(x1)))) -> 0(3(4(0(2(1(x1)))))) 33.00/9.21 4(0(0(5(4(x1))))) -> 5(0(0(4(4(5(x1)))))) 33.00/9.21 4(2(5(4(1(x1))))) -> 4(4(1(5(3(2(x1)))))) 33.00/9.21 1(0(5(4(x1)))) -> 1(4(5(0(3(3(x1)))))) 33.00/9.21 1(0(5(4(x1)))) -> 5(5(1(0(2(4(x1)))))) 33.00/9.21 1(4(2(1(x1)))) -> 4(0(2(1(2(1(x1)))))) 33.00/9.21 1(0(1(2(4(x1))))) -> 1(1(0(2(3(4(x1)))))) 33.00/9.21 1(4(2(1(2(x1))))) -> 0(2(2(1(1(4(x1)))))) 33.00/9.21 33.00/9.21 Q is empty. 33.00/9.21 We have to consider all minimal (P,Q,R)-chains. 33.00/9.21 ---------------------------------------- 33.00/9.21 33.00/9.21 (10) QDPOrderProof (EQUIVALENT) 33.00/9.21 We use the reduction pair processor [LPAR04,JAR06]. 33.00/9.21 33.00/9.21 33.00/9.21 The following pairs can be oriented strictly and are deleted. 33.00/9.21 33.00/9.21 1^1(4(2(1(2(x1))))) -> 1^1(4(x1)) 33.00/9.21 The remaining pairs can at least be oriented weakly. 33.00/9.21 Used ordering: Polynomial interpretation [POLO]: 33.00/9.21 33.00/9.21 POL(0(x_1)) = 0 33.00/9.21 POL(1(x_1)) = x_1 33.00/9.21 POL(1^1(x_1)) = x_1 33.00/9.21 POL(2(x_1)) = 1 + x_1 33.00/9.21 POL(3(x_1)) = 0 33.00/9.21 POL(4(x_1)) = x_1 33.00/9.21 POL(5(x_1)) = 0 33.00/9.21 33.00/9.21 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 33.00/9.21 33.00/9.21 4(2(1(x1))) -> 4(0(2(1(x1)))) 33.00/9.21 4(2(1(x1))) -> 1(2(4(0(2(x1))))) 33.00/9.21 4(1(2(1(x1)))) -> 4(1(0(2(1(x1))))) 33.00/9.21 4(1(2(1(x1)))) -> 3(4(0(2(1(1(x1)))))) 33.00/9.21 4(3(2(1(x1)))) -> 0(3(4(0(2(1(x1)))))) 33.00/9.21 4(0(0(5(4(x1))))) -> 5(0(0(4(4(5(x1)))))) 33.00/9.21 4(2(5(4(1(x1))))) -> 4(4(1(5(3(2(x1)))))) 33.00/9.21 33.00/9.21 33.00/9.21 ---------------------------------------- 33.00/9.21 33.00/9.21 (11) 33.00/9.21 Obligation: 33.00/9.21 Q DP problem: 33.00/9.21 P is empty. 33.00/9.21 The TRS R consists of the following rules: 33.00/9.21 33.00/9.21 4(2(1(x1))) -> 4(0(2(1(x1)))) 33.00/9.21 4(2(1(x1))) -> 1(2(4(0(2(x1))))) 33.00/9.21 4(1(2(1(x1)))) -> 4(1(0(2(1(x1))))) 33.00/9.21 4(1(2(1(x1)))) -> 3(4(0(2(1(1(x1)))))) 33.00/9.21 4(3(2(1(x1)))) -> 0(3(4(0(2(1(x1)))))) 33.00/9.21 4(0(0(5(4(x1))))) -> 5(0(0(4(4(5(x1)))))) 33.00/9.21 4(2(5(4(1(x1))))) -> 4(4(1(5(3(2(x1)))))) 33.00/9.21 1(0(5(4(x1)))) -> 1(4(5(0(3(3(x1)))))) 33.00/9.21 1(0(5(4(x1)))) -> 5(5(1(0(2(4(x1)))))) 33.00/9.21 1(4(2(1(x1)))) -> 4(0(2(1(2(1(x1)))))) 33.00/9.21 1(0(1(2(4(x1))))) -> 1(1(0(2(3(4(x1)))))) 33.00/9.21 1(4(2(1(2(x1))))) -> 0(2(2(1(1(4(x1)))))) 33.00/9.21 33.00/9.21 Q is empty. 33.00/9.21 We have to consider all minimal (P,Q,R)-chains. 33.00/9.21 ---------------------------------------- 33.00/9.21 33.00/9.21 (12) PisEmptyProof (EQUIVALENT) 33.00/9.21 The TRS P is empty. Hence, there is no (P,Q,R) chain. 33.00/9.21 ---------------------------------------- 33.00/9.21 33.00/9.21 (13) 33.00/9.21 YES 33.00/9.21 33.00/9.21 ---------------------------------------- 33.00/9.21 33.00/9.21 (14) 33.00/9.21 Obligation: 33.00/9.21 Q DP problem: 33.00/9.21 The TRS P consists of the following rules: 33.00/9.21 33.00/9.21 0^1(0(5(1(2(x1))))) -> 0^1(1(x1)) 33.00/9.21 33.00/9.21 The TRS R consists of the following rules: 33.00/9.21 33.00/9.21 0(1(1(x1))) -> 1(0(2(1(x1)))) 33.00/9.21 0(1(1(x1))) -> 1(1(0(3(2(x1))))) 33.00/9.21 0(1(1(x1))) -> 1(4(0(0(2(1(x1)))))) 33.00/9.21 0(1(4(x1))) -> 1(4(0(3(x1)))) 33.00/9.21 0(1(4(x1))) -> 4(0(2(1(x1)))) 33.00/9.21 0(1(4(x1))) -> 4(0(2(1(3(x1))))) 33.00/9.21 0(4(1(x1))) -> 0(2(4(1(x1)))) 33.00/9.21 0(4(1(x1))) -> 4(0(2(1(x1)))) 33.00/9.21 0(4(1(x1))) -> 4(0(3(1(x1)))) 33.00/9.21 0(4(1(x1))) -> 1(4(4(0(2(x1))))) 33.00/9.21 0(4(1(x1))) -> 2(1(4(0(2(x1))))) 33.00/9.21 0(5(4(x1))) -> 1(4(0(0(2(5(x1)))))) 33.00/9.21 0(5(4(x1))) -> 4(0(2(5(2(5(x1)))))) 33.00/9.21 0(5(4(x1))) -> 5(0(4(0(3(3(x1)))))) 33.00/9.21 4(2(1(x1))) -> 4(0(2(1(x1)))) 33.00/9.21 4(2(1(x1))) -> 1(2(4(0(2(x1))))) 33.00/9.21 0(1(0(4(x1)))) -> 0(0(2(2(1(4(x1)))))) 33.00/9.21 0(1(1(2(x1)))) -> 5(1(0(2(1(x1))))) 33.00/9.21 0(1(1(3(x1)))) -> 1(1(5(0(3(x1))))) 33.00/9.21 0(1(4(1(x1)))) -> 1(0(2(4(1(x1))))) 33.00/9.21 0(1(4(3(x1)))) -> 1(0(2(4(3(x1))))) 33.00/9.21 0(1(4(3(x1)))) -> 4(0(2(1(3(x1))))) 33.00/9.21 0(4(1(2(x1)))) -> 2(0(3(1(4(x1))))) 33.00/9.21 0(4(2(1(x1)))) -> 0(4(3(0(2(1(x1)))))) 33.00/9.21 0(5(0(4(x1)))) -> 1(5(4(0(0(2(x1)))))) 33.00/9.21 0(5(1(3(x1)))) -> 1(1(5(0(3(x1))))) 33.00/9.21 0(5(1(3(x1)))) -> 5(3(1(0(3(x1))))) 33.00/9.21 0(5(4(1(x1)))) -> 4(1(5(4(0(2(x1)))))) 33.00/9.21 0(5(4(3(x1)))) -> 0(2(5(0(3(4(x1)))))) 33.00/9.21 0(5(4(3(x1)))) -> 1(5(3(4(0(3(x1)))))) 33.00/9.21 1(0(5(4(x1)))) -> 1(4(5(0(3(3(x1)))))) 33.00/9.21 1(0(5(4(x1)))) -> 5(5(1(0(2(4(x1)))))) 33.00/9.21 1(4(2(1(x1)))) -> 4(0(2(1(2(1(x1)))))) 33.00/9.21 4(1(2(1(x1)))) -> 4(1(0(2(1(x1))))) 33.00/9.21 4(1(2(1(x1)))) -> 3(4(0(2(1(1(x1)))))) 33.00/9.21 4(3(2(1(x1)))) -> 0(3(4(0(2(1(x1)))))) 33.00/9.21 0(0(1(2(3(x1))))) -> 1(0(3(0(0(2(x1)))))) 33.00/9.21 0(0(5(1(2(x1))))) -> 0(0(2(5(0(1(x1)))))) 33.00/9.21 0(0(5(1(3(x1))))) -> 4(5(0(0(3(1(x1)))))) 33.00/9.21 0(1(3(4(2(x1))))) -> 1(3(4(3(0(2(x1)))))) 33.00/9.21 0(4(5(3(4(x1))))) -> 0(3(2(5(4(4(x1)))))) 33.00/9.21 0(5(0(2(2(x1))))) -> 0(0(2(5(2(4(x1)))))) 33.00/9.21 0(5(1(1(3(x1))))) -> 0(3(2(1(1(5(x1)))))) 33.00/9.21 0(5(1(4(3(x1))))) -> 3(0(2(1(5(4(x1)))))) 33.00/9.21 0(5(5(1(2(x1))))) -> 1(5(3(0(2(5(x1)))))) 33.00/9.21 1(0(1(2(4(x1))))) -> 1(1(0(2(3(4(x1)))))) 33.00/9.21 1(4(2(1(2(x1))))) -> 0(2(2(1(1(4(x1)))))) 33.00/9.21 4(0(0(5(4(x1))))) -> 5(0(0(4(4(5(x1)))))) 33.00/9.21 4(2(5(4(1(x1))))) -> 4(4(1(5(3(2(x1)))))) 33.00/9.21 33.00/9.21 Q is empty. 33.00/9.21 We have to consider all minimal (P,Q,R)-chains. 33.00/9.21 ---------------------------------------- 33.00/9.21 33.00/9.21 (15) UsableRulesProof (EQUIVALENT) 33.00/9.21 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. 33.00/9.21 ---------------------------------------- 33.00/9.21 33.00/9.21 (16) 33.00/9.21 Obligation: 33.00/9.21 Q DP problem: 33.00/9.21 The TRS P consists of the following rules: 33.00/9.21 33.00/9.21 0^1(0(5(1(2(x1))))) -> 0^1(1(x1)) 33.00/9.21 33.00/9.21 The TRS R consists of the following rules: 33.00/9.21 33.00/9.21 1(0(5(4(x1)))) -> 1(4(5(0(3(3(x1)))))) 33.00/9.21 1(0(5(4(x1)))) -> 5(5(1(0(2(4(x1)))))) 33.00/9.21 1(4(2(1(x1)))) -> 4(0(2(1(2(1(x1)))))) 33.00/9.21 1(0(1(2(4(x1))))) -> 1(1(0(2(3(4(x1)))))) 33.00/9.21 1(4(2(1(2(x1))))) -> 0(2(2(1(1(4(x1)))))) 33.00/9.21 4(2(1(x1))) -> 4(0(2(1(x1)))) 33.00/9.21 4(2(1(x1))) -> 1(2(4(0(2(x1))))) 33.00/9.21 4(1(2(1(x1)))) -> 4(1(0(2(1(x1))))) 33.00/9.21 4(1(2(1(x1)))) -> 3(4(0(2(1(1(x1)))))) 33.00/9.21 4(3(2(1(x1)))) -> 0(3(4(0(2(1(x1)))))) 33.00/9.21 4(0(0(5(4(x1))))) -> 5(0(0(4(4(5(x1)))))) 33.00/9.21 4(2(5(4(1(x1))))) -> 4(4(1(5(3(2(x1)))))) 33.00/9.21 33.00/9.21 Q is empty. 33.00/9.21 We have to consider all minimal (P,Q,R)-chains. 33.00/9.21 ---------------------------------------- 33.00/9.21 33.00/9.21 (17) QDPOrderProof (EQUIVALENT) 33.00/9.21 We use the reduction pair processor [LPAR04,JAR06]. 33.00/9.21 33.00/9.21 33.00/9.21 The following pairs can be oriented strictly and are deleted. 33.00/9.21 33.00/9.21 0^1(0(5(1(2(x1))))) -> 0^1(1(x1)) 33.00/9.21 The remaining pairs can at least be oriented weakly. 33.00/9.21 Used ordering: Polynomial interpretation [POLO]: 33.00/9.21 33.00/9.21 POL(0(x_1)) = 1 + x_1 33.00/9.21 POL(0^1(x_1)) = x_1 33.00/9.21 POL(1(x_1)) = 1 33.00/9.21 POL(2(x_1)) = 0 33.00/9.21 POL(3(x_1)) = 0 33.00/9.21 POL(4(x_1)) = 0 33.00/9.21 POL(5(x_1)) = x_1 33.00/9.21 33.00/9.21 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 33.00/9.21 33.00/9.21 1(0(5(4(x1)))) -> 1(4(5(0(3(3(x1)))))) 33.00/9.21 1(0(5(4(x1)))) -> 5(5(1(0(2(4(x1)))))) 33.00/9.21 1(4(2(1(x1)))) -> 4(0(2(1(2(1(x1)))))) 33.00/9.21 1(0(1(2(4(x1))))) -> 1(1(0(2(3(4(x1)))))) 33.00/9.21 1(4(2(1(2(x1))))) -> 0(2(2(1(1(4(x1)))))) 33.00/9.21 33.00/9.21 33.00/9.21 ---------------------------------------- 33.00/9.21 33.00/9.21 (18) 33.00/9.21 Obligation: 33.00/9.21 Q DP problem: 33.00/9.21 P is empty. 33.00/9.21 The TRS R consists of the following rules: 33.00/9.21 33.00/9.21 1(0(5(4(x1)))) -> 1(4(5(0(3(3(x1)))))) 33.00/9.21 1(0(5(4(x1)))) -> 5(5(1(0(2(4(x1)))))) 33.00/9.21 1(4(2(1(x1)))) -> 4(0(2(1(2(1(x1)))))) 33.00/9.21 1(0(1(2(4(x1))))) -> 1(1(0(2(3(4(x1)))))) 33.00/9.21 1(4(2(1(2(x1))))) -> 0(2(2(1(1(4(x1)))))) 33.00/9.21 4(2(1(x1))) -> 4(0(2(1(x1)))) 33.00/9.21 4(2(1(x1))) -> 1(2(4(0(2(x1))))) 33.00/9.21 4(1(2(1(x1)))) -> 4(1(0(2(1(x1))))) 33.00/9.21 4(1(2(1(x1)))) -> 3(4(0(2(1(1(x1)))))) 33.00/9.21 4(3(2(1(x1)))) -> 0(3(4(0(2(1(x1)))))) 33.00/9.21 4(0(0(5(4(x1))))) -> 5(0(0(4(4(5(x1)))))) 33.00/9.21 4(2(5(4(1(x1))))) -> 4(4(1(5(3(2(x1)))))) 33.00/9.21 33.00/9.21 Q is empty. 33.00/9.21 We have to consider all minimal (P,Q,R)-chains. 33.00/9.21 ---------------------------------------- 33.00/9.21 33.00/9.21 (19) PisEmptyProof (EQUIVALENT) 33.00/9.21 The TRS P is empty. Hence, there is no (P,Q,R) chain. 33.00/9.21 ---------------------------------------- 33.00/9.21 33.00/9.21 (20) 33.00/9.21 YES 33.29/9.28 EOF