11.79/3.78 YES 12.04/3.82 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 12.04/3.82 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 12.04/3.82 12.04/3.82 12.04/3.82 Termination w.r.t. Q of the given QTRS could be proven: 12.04/3.82 12.04/3.82 (0) QTRS 12.04/3.82 (1) QTRSRRRProof [EQUIVALENT, 169 ms] 12.04/3.82 (2) QTRS 12.04/3.82 (3) DependencyPairsProof [EQUIVALENT, 79 ms] 12.04/3.82 (4) QDP 12.04/3.82 (5) DependencyGraphProof [EQUIVALENT, 0 ms] 12.04/3.82 (6) TRUE 12.04/3.82 12.04/3.82 12.04/3.82 ---------------------------------------- 12.04/3.82 12.04/3.82 (0) 12.04/3.82 Obligation: 12.04/3.82 Q restricted rewrite system: 12.04/3.82 The TRS R consists of the following rules: 12.04/3.82 12.04/3.82 0(1(2(1(x1)))) -> 3(3(2(x1))) 12.04/3.82 1(2(3(2(x1)))) -> 3(4(4(2(x1)))) 12.04/3.82 0(5(1(4(1(x1))))) -> 4(1(4(3(x1)))) 12.04/3.82 4(3(0(2(2(x1))))) -> 4(1(1(4(5(x1))))) 12.04/3.82 5(5(1(5(2(x1))))) -> 4(3(5(2(x1)))) 12.04/3.82 0(4(3(3(4(4(1(x1))))))) -> 4(4(2(5(0(2(2(x1))))))) 12.04/3.82 2(0(4(1(2(2(1(3(x1)))))))) -> 2(3(0(4(5(5(1(1(x1)))))))) 12.04/3.82 1(2(2(1(5(2(1(2(1(x1))))))))) -> 1(2(2(2(0(2(4(4(3(x1))))))))) 12.04/3.82 4(5(1(4(3(4(3(5(4(3(x1)))))))))) -> 4(3(2(0(2(4(3(2(3(x1))))))))) 12.04/3.82 1(4(1(2(5(3(4(3(3(2(2(x1))))))))))) -> 0(0(1(4(0(4(5(2(3(0(4(x1))))))))))) 12.04/3.82 4(5(1(3(2(2(5(4(3(5(4(x1))))))))))) -> 4(0(1(1(5(3(5(4(2(2(4(x1))))))))))) 12.04/3.82 5(1(4(0(1(5(5(3(3(0(3(2(x1)))))))))))) -> 3(0(5(3(2(0(1(0(4(1(2(x1))))))))))) 12.04/3.82 0(4(1(1(3(3(2(5(4(2(2(1(3(x1))))))))))))) -> 1(0(1(4(3(4(4(2(3(4(2(2(1(x1))))))))))))) 12.04/3.82 5(1(3(3(5(3(1(3(2(1(2(0(4(x1))))))))))))) -> 2(2(3(2(3(2(3(5(2(5(1(4(x1)))))))))))) 12.04/3.82 0(5(3(5(3(3(3(3(4(5(5(5(4(4(x1)))))))))))))) -> 0(1(0(3(2(3(4(0(5(5(2(4(0(x1))))))))))))) 12.04/3.82 1(5(0(1(0(4(4(2(2(3(4(1(4(1(x1)))))))))))))) -> 3(4(5(0(0(4(0(3(5(0(4(1(5(4(x1)))))))))))))) 12.04/3.82 5(1(0(5(2(2(2(3(3(2(5(1(5(1(x1)))))))))))))) -> 5(4(0(1(4(3(2(2(3(3(3(5(5(1(x1)))))))))))))) 12.04/3.82 5(1(2(2(4(0(2(4(2(5(2(1(4(0(5(x1))))))))))))))) -> 0(1(4(3(0(5(3(4(3(3(1(4(1(5(x1)))))))))))))) 12.04/3.82 0(4(0(3(2(0(2(1(2(0(0(2(4(2(3(4(x1)))))))))))))))) -> 3(2(1(3(3(4(5(5(4(0(3(2(1(2(3(x1))))))))))))))) 12.04/3.82 1(5(1(3(3(3(0(4(0(2(3(1(5(1(4(2(x1)))))))))))))))) -> 3(4(0(5(0(4(4(0(2(1(3(1(4(0(4(2(x1)))))))))))))))) 12.04/3.82 5(1(1(0(0(3(2(5(0(3(4(2(1(2(5(1(x1)))))))))))))))) -> 5(1(3(2(1(0(1(0(5(5(3(1(1(4(1(0(x1)))))))))))))))) 12.04/3.82 3(2(1(2(4(2(1(1(3(3(3(5(2(2(0(4(4(x1))))))))))))))))) -> 3(2(3(1(0(2(0(2(4(5(5(4(1(0(0(2(5(0(x1)))))))))))))))))) 12.04/3.82 4(1(0(3(0(4(3(2(2(1(3(2(2(4(0(2(4(x1))))))))))))))))) -> 4(2(5(3(3(3(1(2(4(5(3(5(3(5(1(3(4(x1))))))))))))))))) 12.04/3.82 3(0(0(2(1(1(3(5(1(2(2(2(5(1(0(0(0(1(x1)))))))))))))))))) -> 3(5(1(0(4(0(1(2(2(5(0(3(4(3(5(5(4(3(x1)))))))))))))))))) 12.04/3.82 4(5(5(1(5(3(5(3(2(0(4(4(2(1(0(3(5(3(x1)))))))))))))))))) -> 4(4(0(5(1(3(5(5(3(4(4(0(0(4(3(0(0(0(x1)))))))))))))))))) 12.04/3.82 4(5(5(2(5(1(0(2(1(0(1(4(4(4(2(1(5(1(x1)))))))))))))))))) -> 4(3(2(3(0(2(5(3(4(1(4(4(5(1(1(4(0(x1))))))))))))))))) 12.04/3.82 0(2(0(2(2(0(1(1(2(4(1(1(0(3(3(2(1(4(1(4(x1)))))))))))))))))))) -> 2(2(3(3(0(2(1(3(5(3(4(4(1(2(4(4(4(4(4(0(x1)))))))))))))))))))) 12.04/3.82 3(4(1(1(0(3(4(0(5(5(5(5(3(5(2(3(2(3(1(3(x1)))))))))))))))))))) -> 3(4(3(4(3(1(0(1(1(4(5(5(2(3(2(3(0(2(3(x1))))))))))))))))))) 12.04/3.82 4(5(2(3(5(4(5(0(5(1(2(3(0(1(1(0(3(5(0(3(0(x1))))))))))))))))))))) -> 4(4(3(1(4(4(0(5(3(5(2(1(4(2(4(1(0(2(4(5(0(x1))))))))))))))))))))) 12.04/3.82 5(1(4(0(0(3(4(2(3(0(3(5(4(0(4(2(4(0(0(5(0(x1))))))))))))))))))))) -> 5(0(3(2(2(0(4(1(1(5(3(0(1(5(0(1(3(2(2(3(x1)))))))))))))))))))) 12.04/3.82 12.04/3.82 Q is empty. 12.04/3.82 12.04/3.82 ---------------------------------------- 12.04/3.82 12.04/3.82 (1) QTRSRRRProof (EQUIVALENT) 12.04/3.82 Used ordering: 12.04/3.82 Polynomial interpretation [POLO]: 12.04/3.82 12.04/3.82 POL(0(x_1)) = 61 + x_1 12.04/3.82 POL(1(x_1)) = 70 + x_1 12.04/3.82 POL(2(x_1)) = 76 + x_1 12.04/3.82 POL(3(x_1)) = 77 + x_1 12.04/3.82 POL(4(x_1)) = 64 + x_1 12.04/3.82 POL(5(x_1)) = 60 + x_1 12.04/3.82 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: 12.04/3.82 12.04/3.82 0(1(2(1(x1)))) -> 3(3(2(x1))) 12.04/3.82 1(2(3(2(x1)))) -> 3(4(4(2(x1)))) 12.04/3.82 0(5(1(4(1(x1))))) -> 4(1(4(3(x1)))) 12.04/3.82 4(3(0(2(2(x1))))) -> 4(1(1(4(5(x1))))) 12.04/3.82 5(5(1(5(2(x1))))) -> 4(3(5(2(x1)))) 12.04/3.82 2(0(4(1(2(2(1(3(x1)))))))) -> 2(3(0(4(5(5(1(1(x1)))))))) 12.04/3.82 1(2(2(1(5(2(1(2(1(x1))))))))) -> 1(2(2(2(0(2(4(4(3(x1))))))))) 12.04/3.82 4(5(1(4(3(4(3(5(4(3(x1)))))))))) -> 4(3(2(0(2(4(3(2(3(x1))))))))) 12.04/3.82 1(4(1(2(5(3(4(3(3(2(2(x1))))))))))) -> 0(0(1(4(0(4(5(2(3(0(4(x1))))))))))) 12.04/3.82 4(5(1(3(2(2(5(4(3(5(4(x1))))))))))) -> 4(0(1(1(5(3(5(4(2(2(4(x1))))))))))) 12.04/3.82 5(1(4(0(1(5(5(3(3(0(3(2(x1)))))))))))) -> 3(0(5(3(2(0(1(0(4(1(2(x1))))))))))) 12.04/3.82 0(4(1(1(3(3(2(5(4(2(2(1(3(x1))))))))))))) -> 1(0(1(4(3(4(4(2(3(4(2(2(1(x1))))))))))))) 12.04/3.82 5(1(3(3(5(3(1(3(2(1(2(0(4(x1))))))))))))) -> 2(2(3(2(3(2(3(5(2(5(1(4(x1)))))))))))) 12.04/3.82 0(5(3(5(3(3(3(3(4(5(5(5(4(4(x1)))))))))))))) -> 0(1(0(3(2(3(4(0(5(5(2(4(0(x1))))))))))))) 12.04/3.82 1(5(0(1(0(4(4(2(2(3(4(1(4(1(x1)))))))))))))) -> 3(4(5(0(0(4(0(3(5(0(4(1(5(4(x1)))))))))))))) 12.04/3.82 5(1(2(2(4(0(2(4(2(5(2(1(4(0(5(x1))))))))))))))) -> 0(1(4(3(0(5(3(4(3(3(1(4(1(5(x1)))))))))))))) 12.04/3.82 0(4(0(3(2(0(2(1(2(0(0(2(4(2(3(4(x1)))))))))))))))) -> 3(2(1(3(3(4(5(5(4(0(3(2(1(2(3(x1))))))))))))))) 12.04/3.82 1(5(1(3(3(3(0(4(0(2(3(1(5(1(4(2(x1)))))))))))))))) -> 3(4(0(5(0(4(4(0(2(1(3(1(4(0(4(2(x1)))))))))))))))) 12.04/3.82 5(1(1(0(0(3(2(5(0(3(4(2(1(2(5(1(x1)))))))))))))))) -> 5(1(3(2(1(0(1(0(5(5(3(1(1(4(1(0(x1)))))))))))))))) 12.04/3.82 4(1(0(3(0(4(3(2(2(1(3(2(2(4(0(2(4(x1))))))))))))))))) -> 4(2(5(3(3(3(1(2(4(5(3(5(3(5(1(3(4(x1))))))))))))))))) 12.04/3.82 3(0(0(2(1(1(3(5(1(2(2(2(5(1(0(0(0(1(x1)))))))))))))))))) -> 3(5(1(0(4(0(1(2(2(5(0(3(4(3(5(5(4(3(x1)))))))))))))))))) 12.04/3.82 4(5(5(1(5(3(5(3(2(0(4(4(2(1(0(3(5(3(x1)))))))))))))))))) -> 4(4(0(5(1(3(5(5(3(4(4(0(0(4(3(0(0(0(x1)))))))))))))))))) 12.04/3.82 4(5(5(2(5(1(0(2(1(0(1(4(4(4(2(1(5(1(x1)))))))))))))))))) -> 4(3(2(3(0(2(5(3(4(1(4(4(5(1(1(4(0(x1))))))))))))))))) 12.04/3.82 0(2(0(2(2(0(1(1(2(4(1(1(0(3(3(2(1(4(1(4(x1)))))))))))))))))))) -> 2(2(3(3(0(2(1(3(5(3(4(4(1(2(4(4(4(4(4(0(x1)))))))))))))))))))) 12.04/3.82 3(4(1(1(0(3(4(0(5(5(5(5(3(5(2(3(2(3(1(3(x1)))))))))))))))))))) -> 3(4(3(4(3(1(0(1(1(4(5(5(2(3(2(3(0(2(3(x1))))))))))))))))))) 12.04/3.82 12.04/3.82 12.04/3.82 12.04/3.82 12.04/3.82 ---------------------------------------- 12.04/3.82 12.04/3.82 (2) 12.04/3.82 Obligation: 12.04/3.82 Q restricted rewrite system: 12.04/3.82 The TRS R consists of the following rules: 12.04/3.82 12.04/3.82 0(4(3(3(4(4(1(x1))))))) -> 4(4(2(5(0(2(2(x1))))))) 12.04/3.82 5(1(0(5(2(2(2(3(3(2(5(1(5(1(x1)))))))))))))) -> 5(4(0(1(4(3(2(2(3(3(3(5(5(1(x1)))))))))))))) 12.04/3.82 3(2(1(2(4(2(1(1(3(3(3(5(2(2(0(4(4(x1))))))))))))))))) -> 3(2(3(1(0(2(0(2(4(5(5(4(1(0(0(2(5(0(x1)))))))))))))))))) 12.04/3.82 4(5(2(3(5(4(5(0(5(1(2(3(0(1(1(0(3(5(0(3(0(x1))))))))))))))))))))) -> 4(4(3(1(4(4(0(5(3(5(2(1(4(2(4(1(0(2(4(5(0(x1))))))))))))))))))))) 12.04/3.82 5(1(4(0(0(3(4(2(3(0(3(5(4(0(4(2(4(0(0(5(0(x1))))))))))))))))))))) -> 5(0(3(2(2(0(4(1(1(5(3(0(1(5(0(1(3(2(2(3(x1)))))))))))))))))))) 12.04/3.82 12.04/3.82 Q is empty. 12.04/3.82 12.04/3.82 ---------------------------------------- 12.04/3.82 12.04/3.82 (3) DependencyPairsProof (EQUIVALENT) 12.04/3.82 Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. 12.04/3.82 ---------------------------------------- 12.04/3.82 12.04/3.82 (4) 12.04/3.82 Obligation: 12.04/3.82 Q DP problem: 12.04/3.82 The TRS P consists of the following rules: 12.04/3.82 12.04/3.82 0^1(4(3(3(4(4(1(x1))))))) -> 4^1(4(2(5(0(2(2(x1))))))) 12.04/3.82 0^1(4(3(3(4(4(1(x1))))))) -> 4^1(2(5(0(2(2(x1)))))) 12.04/3.82 0^1(4(3(3(4(4(1(x1))))))) -> 5^1(0(2(2(x1)))) 12.04/3.82 0^1(4(3(3(4(4(1(x1))))))) -> 0^1(2(2(x1))) 12.04/3.82 5^1(1(0(5(2(2(2(3(3(2(5(1(5(1(x1)))))))))))))) -> 5^1(4(0(1(4(3(2(2(3(3(3(5(5(1(x1)))))))))))))) 12.04/3.82 5^1(1(0(5(2(2(2(3(3(2(5(1(5(1(x1)))))))))))))) -> 4^1(0(1(4(3(2(2(3(3(3(5(5(1(x1))))))))))))) 12.04/3.82 5^1(1(0(5(2(2(2(3(3(2(5(1(5(1(x1)))))))))))))) -> 0^1(1(4(3(2(2(3(3(3(5(5(1(x1)))))))))))) 12.04/3.82 5^1(1(0(5(2(2(2(3(3(2(5(1(5(1(x1)))))))))))))) -> 4^1(3(2(2(3(3(3(5(5(1(x1)))))))))) 12.04/3.82 5^1(1(0(5(2(2(2(3(3(2(5(1(5(1(x1)))))))))))))) -> 3^1(2(2(3(3(3(5(5(1(x1))))))))) 12.04/3.82 5^1(1(0(5(2(2(2(3(3(2(5(1(5(1(x1)))))))))))))) -> 3^1(3(3(5(5(1(x1)))))) 12.04/3.82 5^1(1(0(5(2(2(2(3(3(2(5(1(5(1(x1)))))))))))))) -> 3^1(3(5(5(1(x1))))) 12.04/3.82 5^1(1(0(5(2(2(2(3(3(2(5(1(5(1(x1)))))))))))))) -> 3^1(5(5(1(x1)))) 12.04/3.82 5^1(1(0(5(2(2(2(3(3(2(5(1(5(1(x1)))))))))))))) -> 5^1(5(1(x1))) 12.04/3.82 3^1(2(1(2(4(2(1(1(3(3(3(5(2(2(0(4(4(x1))))))))))))))))) -> 3^1(2(3(1(0(2(0(2(4(5(5(4(1(0(0(2(5(0(x1)))))))))))))))))) 12.04/3.82 3^1(2(1(2(4(2(1(1(3(3(3(5(2(2(0(4(4(x1))))))))))))))))) -> 3^1(1(0(2(0(2(4(5(5(4(1(0(0(2(5(0(x1)))))))))))))))) 12.04/3.82 3^1(2(1(2(4(2(1(1(3(3(3(5(2(2(0(4(4(x1))))))))))))))))) -> 0^1(2(0(2(4(5(5(4(1(0(0(2(5(0(x1)))))))))))))) 12.04/3.82 3^1(2(1(2(4(2(1(1(3(3(3(5(2(2(0(4(4(x1))))))))))))))))) -> 0^1(2(4(5(5(4(1(0(0(2(5(0(x1)))))))))))) 12.04/3.82 3^1(2(1(2(4(2(1(1(3(3(3(5(2(2(0(4(4(x1))))))))))))))))) -> 4^1(5(5(4(1(0(0(2(5(0(x1)))))))))) 12.04/3.82 3^1(2(1(2(4(2(1(1(3(3(3(5(2(2(0(4(4(x1))))))))))))))))) -> 5^1(5(4(1(0(0(2(5(0(x1))))))))) 12.04/3.82 3^1(2(1(2(4(2(1(1(3(3(3(5(2(2(0(4(4(x1))))))))))))))))) -> 5^1(4(1(0(0(2(5(0(x1)))))))) 12.04/3.82 3^1(2(1(2(4(2(1(1(3(3(3(5(2(2(0(4(4(x1))))))))))))))))) -> 4^1(1(0(0(2(5(0(x1))))))) 12.04/3.82 3^1(2(1(2(4(2(1(1(3(3(3(5(2(2(0(4(4(x1))))))))))))))))) -> 0^1(0(2(5(0(x1))))) 12.04/3.82 3^1(2(1(2(4(2(1(1(3(3(3(5(2(2(0(4(4(x1))))))))))))))))) -> 0^1(2(5(0(x1)))) 12.04/3.82 3^1(2(1(2(4(2(1(1(3(3(3(5(2(2(0(4(4(x1))))))))))))))))) -> 5^1(0(x1)) 12.04/3.82 3^1(2(1(2(4(2(1(1(3(3(3(5(2(2(0(4(4(x1))))))))))))))))) -> 0^1(x1) 12.04/3.82 4^1(5(2(3(5(4(5(0(5(1(2(3(0(1(1(0(3(5(0(3(0(x1))))))))))))))))))))) -> 4^1(4(3(1(4(4(0(5(3(5(2(1(4(2(4(1(0(2(4(5(0(x1))))))))))))))))))))) 12.04/3.82 4^1(5(2(3(5(4(5(0(5(1(2(3(0(1(1(0(3(5(0(3(0(x1))))))))))))))))))))) -> 4^1(3(1(4(4(0(5(3(5(2(1(4(2(4(1(0(2(4(5(0(x1)))))))))))))))))))) 12.04/3.82 4^1(5(2(3(5(4(5(0(5(1(2(3(0(1(1(0(3(5(0(3(0(x1))))))))))))))))))))) -> 3^1(1(4(4(0(5(3(5(2(1(4(2(4(1(0(2(4(5(0(x1))))))))))))))))))) 12.04/3.82 4^1(5(2(3(5(4(5(0(5(1(2(3(0(1(1(0(3(5(0(3(0(x1))))))))))))))))))))) -> 4^1(4(0(5(3(5(2(1(4(2(4(1(0(2(4(5(0(x1))))))))))))))))) 12.04/3.82 4^1(5(2(3(5(4(5(0(5(1(2(3(0(1(1(0(3(5(0(3(0(x1))))))))))))))))))))) -> 4^1(0(5(3(5(2(1(4(2(4(1(0(2(4(5(0(x1)))))))))))))))) 12.04/3.82 4^1(5(2(3(5(4(5(0(5(1(2(3(0(1(1(0(3(5(0(3(0(x1))))))))))))))))))))) -> 0^1(5(3(5(2(1(4(2(4(1(0(2(4(5(0(x1))))))))))))))) 12.04/3.82 4^1(5(2(3(5(4(5(0(5(1(2(3(0(1(1(0(3(5(0(3(0(x1))))))))))))))))))))) -> 5^1(3(5(2(1(4(2(4(1(0(2(4(5(0(x1)))))))))))))) 12.04/3.82 4^1(5(2(3(5(4(5(0(5(1(2(3(0(1(1(0(3(5(0(3(0(x1))))))))))))))))))))) -> 3^1(5(2(1(4(2(4(1(0(2(4(5(0(x1))))))))))))) 12.04/3.82 4^1(5(2(3(5(4(5(0(5(1(2(3(0(1(1(0(3(5(0(3(0(x1))))))))))))))))))))) -> 5^1(2(1(4(2(4(1(0(2(4(5(0(x1)))))))))))) 12.04/3.82 4^1(5(2(3(5(4(5(0(5(1(2(3(0(1(1(0(3(5(0(3(0(x1))))))))))))))))))))) -> 4^1(2(4(1(0(2(4(5(0(x1))))))))) 12.04/3.82 4^1(5(2(3(5(4(5(0(5(1(2(3(0(1(1(0(3(5(0(3(0(x1))))))))))))))))))))) -> 4^1(1(0(2(4(5(0(x1))))))) 12.04/3.82 4^1(5(2(3(5(4(5(0(5(1(2(3(0(1(1(0(3(5(0(3(0(x1))))))))))))))))))))) -> 0^1(2(4(5(0(x1))))) 12.04/3.82 4^1(5(2(3(5(4(5(0(5(1(2(3(0(1(1(0(3(5(0(3(0(x1))))))))))))))))))))) -> 4^1(5(0(x1))) 12.04/3.82 4^1(5(2(3(5(4(5(0(5(1(2(3(0(1(1(0(3(5(0(3(0(x1))))))))))))))))))))) -> 5^1(0(x1)) 12.04/3.82 5^1(1(4(0(0(3(4(2(3(0(3(5(4(0(4(2(4(0(0(5(0(x1))))))))))))))))))))) -> 5^1(0(3(2(2(0(4(1(1(5(3(0(1(5(0(1(3(2(2(3(x1)))))))))))))))))))) 12.04/3.82 5^1(1(4(0(0(3(4(2(3(0(3(5(4(0(4(2(4(0(0(5(0(x1))))))))))))))))))))) -> 0^1(3(2(2(0(4(1(1(5(3(0(1(5(0(1(3(2(2(3(x1))))))))))))))))))) 12.04/3.82 5^1(1(4(0(0(3(4(2(3(0(3(5(4(0(4(2(4(0(0(5(0(x1))))))))))))))))))))) -> 3^1(2(2(0(4(1(1(5(3(0(1(5(0(1(3(2(2(3(x1)))))))))))))))))) 12.04/3.82 5^1(1(4(0(0(3(4(2(3(0(3(5(4(0(4(2(4(0(0(5(0(x1))))))))))))))))))))) -> 0^1(4(1(1(5(3(0(1(5(0(1(3(2(2(3(x1))))))))))))))) 12.04/3.82 5^1(1(4(0(0(3(4(2(3(0(3(5(4(0(4(2(4(0(0(5(0(x1))))))))))))))))))))) -> 4^1(1(1(5(3(0(1(5(0(1(3(2(2(3(x1)))))))))))))) 12.04/3.82 5^1(1(4(0(0(3(4(2(3(0(3(5(4(0(4(2(4(0(0(5(0(x1))))))))))))))))))))) -> 5^1(3(0(1(5(0(1(3(2(2(3(x1))))))))))) 12.04/3.82 5^1(1(4(0(0(3(4(2(3(0(3(5(4(0(4(2(4(0(0(5(0(x1))))))))))))))))))))) -> 3^1(0(1(5(0(1(3(2(2(3(x1)))))))))) 12.04/3.82 5^1(1(4(0(0(3(4(2(3(0(3(5(4(0(4(2(4(0(0(5(0(x1))))))))))))))))))))) -> 0^1(1(5(0(1(3(2(2(3(x1))))))))) 12.04/3.82 5^1(1(4(0(0(3(4(2(3(0(3(5(4(0(4(2(4(0(0(5(0(x1))))))))))))))))))))) -> 5^1(0(1(3(2(2(3(x1))))))) 12.04/3.82 5^1(1(4(0(0(3(4(2(3(0(3(5(4(0(4(2(4(0(0(5(0(x1))))))))))))))))))))) -> 0^1(1(3(2(2(3(x1)))))) 12.04/3.82 5^1(1(4(0(0(3(4(2(3(0(3(5(4(0(4(2(4(0(0(5(0(x1))))))))))))))))))))) -> 3^1(2(2(3(x1)))) 12.04/3.82 5^1(1(4(0(0(3(4(2(3(0(3(5(4(0(4(2(4(0(0(5(0(x1))))))))))))))))))))) -> 3^1(x1) 12.04/3.82 12.04/3.82 The TRS R consists of the following rules: 12.04/3.82 12.04/3.82 0(4(3(3(4(4(1(x1))))))) -> 4(4(2(5(0(2(2(x1))))))) 12.04/3.82 5(1(0(5(2(2(2(3(3(2(5(1(5(1(x1)))))))))))))) -> 5(4(0(1(4(3(2(2(3(3(3(5(5(1(x1)))))))))))))) 12.04/3.82 3(2(1(2(4(2(1(1(3(3(3(5(2(2(0(4(4(x1))))))))))))))))) -> 3(2(3(1(0(2(0(2(4(5(5(4(1(0(0(2(5(0(x1)))))))))))))))))) 12.04/3.82 4(5(2(3(5(4(5(0(5(1(2(3(0(1(1(0(3(5(0(3(0(x1))))))))))))))))))))) -> 4(4(3(1(4(4(0(5(3(5(2(1(4(2(4(1(0(2(4(5(0(x1))))))))))))))))))))) 12.04/3.82 5(1(4(0(0(3(4(2(3(0(3(5(4(0(4(2(4(0(0(5(0(x1))))))))))))))))))))) -> 5(0(3(2(2(0(4(1(1(5(3(0(1(5(0(1(3(2(2(3(x1)))))))))))))))))))) 12.04/3.82 12.04/3.82 Q is empty. 12.04/3.82 We have to consider all minimal (P,Q,R)-chains. 12.04/3.82 ---------------------------------------- 12.04/3.82 12.04/3.82 (5) DependencyGraphProof (EQUIVALENT) 12.04/3.82 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 51 less nodes. 12.04/3.82 ---------------------------------------- 12.04/3.82 12.04/3.82 (6) 12.04/3.82 TRUE 12.09/3.86 EOF