11.64/3.83 YES 11.64/3.88 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 11.64/3.88 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 11.64/3.88 11.64/3.88 11.64/3.88 Termination w.r.t. Q of the given QTRS could be proven: 11.64/3.88 11.64/3.88 (0) QTRS 11.64/3.88 (1) QTRSRRRProof [EQUIVALENT, 134 ms] 11.64/3.88 (2) QTRS 11.64/3.88 (3) DependencyPairsProof [EQUIVALENT, 86 ms] 11.64/3.88 (4) QDP 11.64/3.88 (5) DependencyGraphProof [EQUIVALENT, 1 ms] 11.64/3.88 (6) TRUE 11.64/3.88 11.64/3.88 11.64/3.88 ---------------------------------------- 11.64/3.88 11.64/3.88 (0) 11.64/3.88 Obligation: 11.64/3.88 Q restricted rewrite system: 11.64/3.88 The TRS R consists of the following rules: 11.64/3.88 11.64/3.88 0(1(2(3(x1)))) -> 0(2(2(3(x1)))) 11.64/3.88 1(1(4(4(5(x1))))) -> 5(1(0(0(5(x1))))) 11.64/3.88 2(3(3(2(5(x1))))) -> 3(5(4(5(5(x1))))) 11.64/3.88 5(1(1(5(3(x1))))) -> 5(1(4(5(3(x1))))) 11.64/3.88 0(2(5(1(1(4(x1)))))) -> 0(3(2(2(4(5(x1)))))) 11.64/3.88 1(2(1(4(0(3(x1)))))) -> 4(2(5(4(5(3(x1)))))) 11.64/3.88 1(5(2(0(4(3(x1)))))) -> 5(0(1(1(1(x1))))) 11.64/3.88 2(2(1(5(4(0(x1)))))) -> 2(3(5(4(0(3(x1)))))) 11.64/3.88 4(0(2(3(1(4(4(x1))))))) -> 4(1(3(0(5(0(5(x1))))))) 11.64/3.88 4(3(5(4(3(2(2(2(x1)))))))) -> 4(1(2(3(4(1(4(x1))))))) 11.64/3.88 0(2(2(2(3(4(3(3(3(x1))))))))) -> 0(5(4(0(5(3(5(5(3(x1))))))))) 11.64/3.88 4(5(3(4(1(1(0(5(2(x1))))))))) -> 4(4(3(1(3(2(0(5(2(x1))))))))) 11.64/3.88 3(3(4(1(0(4(5(1(5(2(x1)))))))))) -> 3(3(4(1(5(0(3(0(2(4(x1)))))))))) 11.64/3.88 2(4(5(4(0(5(5(1(2(1(4(2(x1)))))))))))) -> 4(1(0(1(1(3(3(0(1(4(2(x1))))))))))) 11.64/3.88 1(0(0(4(5(4(3(4(5(1(5(4(0(x1))))))))))))) -> 5(3(3(1(2(1(1(0(3(1(3(x1))))))))))) 11.64/3.88 1(2(2(1(2(3(2(4(4(0(0(3(2(x1))))))))))))) -> 4(4(4(3(2(0(1(3(1(2(2(4(5(x1))))))))))))) 11.64/3.88 4(1(5(4(5(3(3(3(1(2(0(2(0(x1))))))))))))) -> 4(1(4(3(4(4(0(1(3(1(1(5(x1)))))))))))) 11.64/3.88 2(2(3(3(0(2(0(2(5(0(5(5(5(1(0(3(1(x1))))))))))))))))) -> 5(5(5(2(0(2(5(0(0(4(3(2(1(4(3(3(1(x1))))))))))))))))) 11.64/3.88 1(5(1(1(3(0(3(3(3(3(1(1(5(1(5(2(5(2(x1)))))))))))))))))) -> 3(5(4(2(0(5(1(3(4(1(1(2(5(2(4(1(5(2(x1)))))))))))))))))) 11.64/3.88 2(4(3(3(4(2(3(5(4(0(4(0(2(3(0(3(3(0(x1)))))))))))))))))) -> 2(1(3(0(4(4(1(5(2(1(0(3(0(5(0(1(5(x1))))))))))))))))) 11.64/3.88 2(5(5(1(2(3(5(0(3(0(0(3(3(1(0(1(3(2(x1)))))))))))))))))) -> 2(1(5(0(0(1(5(2(2(2(3(1(0(5(0(4(3(3(x1)))))))))))))))))) 11.64/3.88 2(3(5(1(3(0(0(5(0(2(2(4(5(4(0(3(1(4(2(x1))))))))))))))))))) -> 5(2(0(2(0(3(2(3(5(2(2(4(1(3(5(5(1(2(x1)))))))))))))))))) 11.64/3.88 3(2(3(4(1(2(5(5(0(1(2(3(4(0(5(1(4(4(5(4(x1)))))))))))))))))))) -> 3(2(0(1(5(0(1(5(5(1(2(3(0(2(4(2(5(2(2(4(x1)))))))))))))))))))) 11.64/3.88 3(5(5(2(0(4(4(5(5(0(3(5(2(1(2(1(0(2(2(3(x1)))))))))))))))))))) -> 3(1(3(3(0(5(4(2(4(1(2(3(5(0(3(4(5(2(4(3(x1)))))))))))))))))))) 11.64/3.88 4(5(1(4(5(3(1(5(5(3(5(0(2(1(2(4(4(5(1(0(4(x1))))))))))))))))))))) -> 4(4(0(2(1(5(2(0(4(5(2(2(3(5(5(2(2(0(3(5(4(x1))))))))))))))))))))) 11.64/3.88 11.64/3.88 Q is empty. 11.64/3.88 11.64/3.88 ---------------------------------------- 11.64/3.88 11.64/3.88 (1) QTRSRRRProof (EQUIVALENT) 11.64/3.88 Used ordering: 11.64/3.88 Polynomial interpretation [POLO]: 11.64/3.88 11.64/3.88 POL(0(x_1)) = 5 + x_1 11.64/3.88 POL(1(x_1)) = 6 + x_1 11.64/3.88 POL(2(x_1)) = 5 + x_1 11.64/3.88 POL(3(x_1)) = 5 + x_1 11.64/3.88 POL(4(x_1)) = 5 + x_1 11.64/3.88 POL(5(x_1)) = 5 + x_1 11.64/3.88 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: 11.64/3.88 11.64/3.88 0(1(2(3(x1)))) -> 0(2(2(3(x1)))) 11.64/3.88 1(1(4(4(5(x1))))) -> 5(1(0(0(5(x1))))) 11.64/3.88 5(1(1(5(3(x1))))) -> 5(1(4(5(3(x1))))) 11.64/3.88 0(2(5(1(1(4(x1)))))) -> 0(3(2(2(4(5(x1)))))) 11.64/3.88 1(2(1(4(0(3(x1)))))) -> 4(2(5(4(5(3(x1)))))) 11.64/3.88 1(5(2(0(4(3(x1)))))) -> 5(0(1(1(1(x1))))) 11.64/3.88 2(2(1(5(4(0(x1)))))) -> 2(3(5(4(0(3(x1)))))) 11.64/3.88 4(3(5(4(3(2(2(2(x1)))))))) -> 4(1(2(3(4(1(4(x1))))))) 11.64/3.88 4(5(3(4(1(1(0(5(2(x1))))))))) -> 4(4(3(1(3(2(0(5(2(x1))))))))) 11.64/3.88 3(3(4(1(0(4(5(1(5(2(x1)))))))))) -> 3(3(4(1(5(0(3(0(2(4(x1)))))))))) 11.64/3.88 2(4(5(4(0(5(5(1(2(1(4(2(x1)))))))))))) -> 4(1(0(1(1(3(3(0(1(4(2(x1))))))))))) 11.64/3.88 1(0(0(4(5(4(3(4(5(1(5(4(0(x1))))))))))))) -> 5(3(3(1(2(1(1(0(3(1(3(x1))))))))))) 11.64/3.88 4(1(5(4(5(3(3(3(1(2(0(2(0(x1))))))))))))) -> 4(1(4(3(4(4(0(1(3(1(1(5(x1)))))))))))) 11.64/3.88 1(5(1(1(3(0(3(3(3(3(1(1(5(1(5(2(5(2(x1)))))))))))))))))) -> 3(5(4(2(0(5(1(3(4(1(1(2(5(2(4(1(5(2(x1)))))))))))))))))) 11.64/3.88 2(4(3(3(4(2(3(5(4(0(4(0(2(3(0(3(3(0(x1)))))))))))))))))) -> 2(1(3(0(4(4(1(5(2(1(0(3(0(5(0(1(5(x1))))))))))))))))) 11.64/3.88 2(3(5(1(3(0(0(5(0(2(2(4(5(4(0(3(1(4(2(x1))))))))))))))))))) -> 5(2(0(2(0(3(2(3(5(2(2(4(1(3(5(5(1(2(x1)))))))))))))))))) 11.64/3.88 4(5(1(4(5(3(1(5(5(3(5(0(2(1(2(4(4(5(1(0(4(x1))))))))))))))))))))) -> 4(4(0(2(1(5(2(0(4(5(2(2(3(5(5(2(2(0(3(5(4(x1))))))))))))))))))))) 11.64/3.88 11.64/3.88 11.64/3.88 11.64/3.88 11.64/3.88 ---------------------------------------- 11.64/3.88 11.64/3.88 (2) 11.64/3.88 Obligation: 11.64/3.88 Q restricted rewrite system: 11.64/3.88 The TRS R consists of the following rules: 11.64/3.88 11.64/3.88 2(3(3(2(5(x1))))) -> 3(5(4(5(5(x1))))) 11.64/3.88 4(0(2(3(1(4(4(x1))))))) -> 4(1(3(0(5(0(5(x1))))))) 11.64/3.88 0(2(2(2(3(4(3(3(3(x1))))))))) -> 0(5(4(0(5(3(5(5(3(x1))))))))) 11.64/3.88 1(2(2(1(2(3(2(4(4(0(0(3(2(x1))))))))))))) -> 4(4(4(3(2(0(1(3(1(2(2(4(5(x1))))))))))))) 11.64/3.88 2(2(3(3(0(2(0(2(5(0(5(5(5(1(0(3(1(x1))))))))))))))))) -> 5(5(5(2(0(2(5(0(0(4(3(2(1(4(3(3(1(x1))))))))))))))))) 11.64/3.88 2(5(5(1(2(3(5(0(3(0(0(3(3(1(0(1(3(2(x1)))))))))))))))))) -> 2(1(5(0(0(1(5(2(2(2(3(1(0(5(0(4(3(3(x1)))))))))))))))))) 11.64/3.88 3(2(3(4(1(2(5(5(0(1(2(3(4(0(5(1(4(4(5(4(x1)))))))))))))))))))) -> 3(2(0(1(5(0(1(5(5(1(2(3(0(2(4(2(5(2(2(4(x1)))))))))))))))))))) 11.64/3.88 3(5(5(2(0(4(4(5(5(0(3(5(2(1(2(1(0(2(2(3(x1)))))))))))))))))))) -> 3(1(3(3(0(5(4(2(4(1(2(3(5(0(3(4(5(2(4(3(x1)))))))))))))))))))) 11.64/3.88 11.64/3.88 Q is empty. 11.64/3.88 11.64/3.88 ---------------------------------------- 11.64/3.88 11.64/3.88 (3) DependencyPairsProof (EQUIVALENT) 11.64/3.88 Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. 11.64/3.88 ---------------------------------------- 11.64/3.88 11.64/3.88 (4) 11.64/3.88 Obligation: 11.64/3.88 Q DP problem: 11.64/3.88 The TRS P consists of the following rules: 11.64/3.88 11.64/3.88 2^1(3(3(2(5(x1))))) -> 3^1(5(4(5(5(x1))))) 11.64/3.88 2^1(3(3(2(5(x1))))) -> 4^1(5(5(x1))) 11.64/3.88 4^1(0(2(3(1(4(4(x1))))))) -> 4^1(1(3(0(5(0(5(x1))))))) 11.64/3.88 4^1(0(2(3(1(4(4(x1))))))) -> 1^1(3(0(5(0(5(x1)))))) 11.64/3.88 4^1(0(2(3(1(4(4(x1))))))) -> 3^1(0(5(0(5(x1))))) 11.64/3.88 4^1(0(2(3(1(4(4(x1))))))) -> 0^1(5(0(5(x1)))) 11.64/3.88 4^1(0(2(3(1(4(4(x1))))))) -> 0^1(5(x1)) 11.64/3.88 0^1(2(2(2(3(4(3(3(3(x1))))))))) -> 0^1(5(4(0(5(3(5(5(3(x1))))))))) 11.64/3.88 0^1(2(2(2(3(4(3(3(3(x1))))))))) -> 4^1(0(5(3(5(5(3(x1))))))) 11.64/3.88 0^1(2(2(2(3(4(3(3(3(x1))))))))) -> 0^1(5(3(5(5(3(x1)))))) 11.64/3.88 0^1(2(2(2(3(4(3(3(3(x1))))))))) -> 3^1(5(5(3(x1)))) 11.64/3.88 1^1(2(2(1(2(3(2(4(4(0(0(3(2(x1))))))))))))) -> 4^1(4(4(3(2(0(1(3(1(2(2(4(5(x1))))))))))))) 11.64/3.88 1^1(2(2(1(2(3(2(4(4(0(0(3(2(x1))))))))))))) -> 4^1(4(3(2(0(1(3(1(2(2(4(5(x1)))))))))))) 11.64/3.88 1^1(2(2(1(2(3(2(4(4(0(0(3(2(x1))))))))))))) -> 4^1(3(2(0(1(3(1(2(2(4(5(x1))))))))))) 11.64/3.88 1^1(2(2(1(2(3(2(4(4(0(0(3(2(x1))))))))))))) -> 3^1(2(0(1(3(1(2(2(4(5(x1)))))))))) 11.64/3.88 1^1(2(2(1(2(3(2(4(4(0(0(3(2(x1))))))))))))) -> 2^1(0(1(3(1(2(2(4(5(x1))))))))) 11.64/3.88 1^1(2(2(1(2(3(2(4(4(0(0(3(2(x1))))))))))))) -> 0^1(1(3(1(2(2(4(5(x1)))))))) 11.64/3.88 1^1(2(2(1(2(3(2(4(4(0(0(3(2(x1))))))))))))) -> 1^1(3(1(2(2(4(5(x1))))))) 11.64/3.88 1^1(2(2(1(2(3(2(4(4(0(0(3(2(x1))))))))))))) -> 3^1(1(2(2(4(5(x1)))))) 11.64/3.88 1^1(2(2(1(2(3(2(4(4(0(0(3(2(x1))))))))))))) -> 1^1(2(2(4(5(x1))))) 11.64/3.88 1^1(2(2(1(2(3(2(4(4(0(0(3(2(x1))))))))))))) -> 2^1(2(4(5(x1)))) 11.64/3.88 1^1(2(2(1(2(3(2(4(4(0(0(3(2(x1))))))))))))) -> 2^1(4(5(x1))) 11.64/3.88 1^1(2(2(1(2(3(2(4(4(0(0(3(2(x1))))))))))))) -> 4^1(5(x1)) 11.64/3.88 2^1(2(3(3(0(2(0(2(5(0(5(5(5(1(0(3(1(x1))))))))))))))))) -> 2^1(0(2(5(0(0(4(3(2(1(4(3(3(1(x1)))))))))))))) 11.64/3.88 2^1(2(3(3(0(2(0(2(5(0(5(5(5(1(0(3(1(x1))))))))))))))))) -> 0^1(2(5(0(0(4(3(2(1(4(3(3(1(x1))))))))))))) 11.64/3.88 2^1(2(3(3(0(2(0(2(5(0(5(5(5(1(0(3(1(x1))))))))))))))))) -> 2^1(5(0(0(4(3(2(1(4(3(3(1(x1)))))))))))) 11.64/3.88 2^1(2(3(3(0(2(0(2(5(0(5(5(5(1(0(3(1(x1))))))))))))))))) -> 0^1(0(4(3(2(1(4(3(3(1(x1)))))))))) 11.64/3.88 2^1(2(3(3(0(2(0(2(5(0(5(5(5(1(0(3(1(x1))))))))))))))))) -> 0^1(4(3(2(1(4(3(3(1(x1))))))))) 11.64/3.88 2^1(2(3(3(0(2(0(2(5(0(5(5(5(1(0(3(1(x1))))))))))))))))) -> 4^1(3(2(1(4(3(3(1(x1)))))))) 11.64/3.88 2^1(2(3(3(0(2(0(2(5(0(5(5(5(1(0(3(1(x1))))))))))))))))) -> 3^1(2(1(4(3(3(1(x1))))))) 11.64/3.88 2^1(2(3(3(0(2(0(2(5(0(5(5(5(1(0(3(1(x1))))))))))))))))) -> 2^1(1(4(3(3(1(x1)))))) 11.64/3.88 2^1(2(3(3(0(2(0(2(5(0(5(5(5(1(0(3(1(x1))))))))))))))))) -> 1^1(4(3(3(1(x1))))) 11.64/3.88 2^1(2(3(3(0(2(0(2(5(0(5(5(5(1(0(3(1(x1))))))))))))))))) -> 4^1(3(3(1(x1)))) 11.64/3.88 2^1(2(3(3(0(2(0(2(5(0(5(5(5(1(0(3(1(x1))))))))))))))))) -> 3^1(3(1(x1))) 11.64/3.88 2^1(5(5(1(2(3(5(0(3(0(0(3(3(1(0(1(3(2(x1)))))))))))))))))) -> 2^1(1(5(0(0(1(5(2(2(2(3(1(0(5(0(4(3(3(x1)))))))))))))))))) 11.64/3.88 2^1(5(5(1(2(3(5(0(3(0(0(3(3(1(0(1(3(2(x1)))))))))))))))))) -> 1^1(5(0(0(1(5(2(2(2(3(1(0(5(0(4(3(3(x1))))))))))))))))) 11.64/3.88 2^1(5(5(1(2(3(5(0(3(0(0(3(3(1(0(1(3(2(x1)))))))))))))))))) -> 0^1(0(1(5(2(2(2(3(1(0(5(0(4(3(3(x1))))))))))))))) 11.64/3.88 2^1(5(5(1(2(3(5(0(3(0(0(3(3(1(0(1(3(2(x1)))))))))))))))))) -> 0^1(1(5(2(2(2(3(1(0(5(0(4(3(3(x1)))))))))))))) 11.64/3.88 2^1(5(5(1(2(3(5(0(3(0(0(3(3(1(0(1(3(2(x1)))))))))))))))))) -> 1^1(5(2(2(2(3(1(0(5(0(4(3(3(x1))))))))))))) 11.64/3.88 2^1(5(5(1(2(3(5(0(3(0(0(3(3(1(0(1(3(2(x1)))))))))))))))))) -> 2^1(2(2(3(1(0(5(0(4(3(3(x1))))))))))) 11.64/3.88 2^1(5(5(1(2(3(5(0(3(0(0(3(3(1(0(1(3(2(x1)))))))))))))))))) -> 2^1(2(3(1(0(5(0(4(3(3(x1)))))))))) 11.64/3.88 2^1(5(5(1(2(3(5(0(3(0(0(3(3(1(0(1(3(2(x1)))))))))))))))))) -> 2^1(3(1(0(5(0(4(3(3(x1))))))))) 11.64/3.88 2^1(5(5(1(2(3(5(0(3(0(0(3(3(1(0(1(3(2(x1)))))))))))))))))) -> 3^1(1(0(5(0(4(3(3(x1)))))))) 11.64/3.88 2^1(5(5(1(2(3(5(0(3(0(0(3(3(1(0(1(3(2(x1)))))))))))))))))) -> 1^1(0(5(0(4(3(3(x1))))))) 11.64/3.88 2^1(5(5(1(2(3(5(0(3(0(0(3(3(1(0(1(3(2(x1)))))))))))))))))) -> 0^1(5(0(4(3(3(x1)))))) 11.64/3.88 2^1(5(5(1(2(3(5(0(3(0(0(3(3(1(0(1(3(2(x1)))))))))))))))))) -> 0^1(4(3(3(x1)))) 11.64/3.88 2^1(5(5(1(2(3(5(0(3(0(0(3(3(1(0(1(3(2(x1)))))))))))))))))) -> 4^1(3(3(x1))) 11.64/3.88 2^1(5(5(1(2(3(5(0(3(0(0(3(3(1(0(1(3(2(x1)))))))))))))))))) -> 3^1(3(x1)) 11.64/3.88 2^1(5(5(1(2(3(5(0(3(0(0(3(3(1(0(1(3(2(x1)))))))))))))))))) -> 3^1(x1) 11.64/3.88 3^1(2(3(4(1(2(5(5(0(1(2(3(4(0(5(1(4(4(5(4(x1)))))))))))))))))))) -> 3^1(2(0(1(5(0(1(5(5(1(2(3(0(2(4(2(5(2(2(4(x1)))))))))))))))))))) 11.64/3.88 3^1(2(3(4(1(2(5(5(0(1(2(3(4(0(5(1(4(4(5(4(x1)))))))))))))))))))) -> 2^1(0(1(5(0(1(5(5(1(2(3(0(2(4(2(5(2(2(4(x1))))))))))))))))))) 11.64/3.88 3^1(2(3(4(1(2(5(5(0(1(2(3(4(0(5(1(4(4(5(4(x1)))))))))))))))))))) -> 0^1(1(5(0(1(5(5(1(2(3(0(2(4(2(5(2(2(4(x1)))))))))))))))))) 11.64/3.88 3^1(2(3(4(1(2(5(5(0(1(2(3(4(0(5(1(4(4(5(4(x1)))))))))))))))))))) -> 1^1(5(0(1(5(5(1(2(3(0(2(4(2(5(2(2(4(x1))))))))))))))))) 11.64/3.88 3^1(2(3(4(1(2(5(5(0(1(2(3(4(0(5(1(4(4(5(4(x1)))))))))))))))))))) -> 0^1(1(5(5(1(2(3(0(2(4(2(5(2(2(4(x1))))))))))))))) 11.64/3.88 3^1(2(3(4(1(2(5(5(0(1(2(3(4(0(5(1(4(4(5(4(x1)))))))))))))))))))) -> 1^1(5(5(1(2(3(0(2(4(2(5(2(2(4(x1)))))))))))))) 11.64/3.88 3^1(2(3(4(1(2(5(5(0(1(2(3(4(0(5(1(4(4(5(4(x1)))))))))))))))))))) -> 1^1(2(3(0(2(4(2(5(2(2(4(x1))))))))))) 11.64/3.88 3^1(2(3(4(1(2(5(5(0(1(2(3(4(0(5(1(4(4(5(4(x1)))))))))))))))))))) -> 2^1(3(0(2(4(2(5(2(2(4(x1)))))))))) 11.64/3.88 3^1(2(3(4(1(2(5(5(0(1(2(3(4(0(5(1(4(4(5(4(x1)))))))))))))))))))) -> 3^1(0(2(4(2(5(2(2(4(x1))))))))) 11.64/3.88 3^1(2(3(4(1(2(5(5(0(1(2(3(4(0(5(1(4(4(5(4(x1)))))))))))))))))))) -> 0^1(2(4(2(5(2(2(4(x1)))))))) 11.64/3.88 3^1(2(3(4(1(2(5(5(0(1(2(3(4(0(5(1(4(4(5(4(x1)))))))))))))))))))) -> 2^1(4(2(5(2(2(4(x1))))))) 11.64/3.88 3^1(2(3(4(1(2(5(5(0(1(2(3(4(0(5(1(4(4(5(4(x1)))))))))))))))))))) -> 4^1(2(5(2(2(4(x1)))))) 11.64/3.88 3^1(2(3(4(1(2(5(5(0(1(2(3(4(0(5(1(4(4(5(4(x1)))))))))))))))))))) -> 2^1(5(2(2(4(x1))))) 11.64/3.88 3^1(2(3(4(1(2(5(5(0(1(2(3(4(0(5(1(4(4(5(4(x1)))))))))))))))))))) -> 2^1(2(4(x1))) 11.64/3.88 3^1(2(3(4(1(2(5(5(0(1(2(3(4(0(5(1(4(4(5(4(x1)))))))))))))))))))) -> 2^1(4(x1)) 11.64/3.88 3^1(5(5(2(0(4(4(5(5(0(3(5(2(1(2(1(0(2(2(3(x1)))))))))))))))))))) -> 3^1(1(3(3(0(5(4(2(4(1(2(3(5(0(3(4(5(2(4(3(x1)))))))))))))))))))) 11.64/3.88 3^1(5(5(2(0(4(4(5(5(0(3(5(2(1(2(1(0(2(2(3(x1)))))))))))))))))))) -> 1^1(3(3(0(5(4(2(4(1(2(3(5(0(3(4(5(2(4(3(x1))))))))))))))))))) 11.64/3.88 3^1(5(5(2(0(4(4(5(5(0(3(5(2(1(2(1(0(2(2(3(x1)))))))))))))))))))) -> 3^1(3(0(5(4(2(4(1(2(3(5(0(3(4(5(2(4(3(x1)))))))))))))))))) 11.64/3.88 3^1(5(5(2(0(4(4(5(5(0(3(5(2(1(2(1(0(2(2(3(x1)))))))))))))))))))) -> 3^1(0(5(4(2(4(1(2(3(5(0(3(4(5(2(4(3(x1))))))))))))))))) 11.64/3.88 3^1(5(5(2(0(4(4(5(5(0(3(5(2(1(2(1(0(2(2(3(x1)))))))))))))))))))) -> 0^1(5(4(2(4(1(2(3(5(0(3(4(5(2(4(3(x1)))))))))))))))) 11.64/3.88 3^1(5(5(2(0(4(4(5(5(0(3(5(2(1(2(1(0(2(2(3(x1)))))))))))))))))))) -> 4^1(2(4(1(2(3(5(0(3(4(5(2(4(3(x1)))))))))))))) 11.64/3.88 3^1(5(5(2(0(4(4(5(5(0(3(5(2(1(2(1(0(2(2(3(x1)))))))))))))))))))) -> 2^1(4(1(2(3(5(0(3(4(5(2(4(3(x1))))))))))))) 11.64/3.88 3^1(5(5(2(0(4(4(5(5(0(3(5(2(1(2(1(0(2(2(3(x1)))))))))))))))))))) -> 4^1(1(2(3(5(0(3(4(5(2(4(3(x1)))))))))))) 11.64/3.88 3^1(5(5(2(0(4(4(5(5(0(3(5(2(1(2(1(0(2(2(3(x1)))))))))))))))))))) -> 1^1(2(3(5(0(3(4(5(2(4(3(x1))))))))))) 11.64/3.88 3^1(5(5(2(0(4(4(5(5(0(3(5(2(1(2(1(0(2(2(3(x1)))))))))))))))))))) -> 2^1(3(5(0(3(4(5(2(4(3(x1)))))))))) 11.64/3.88 3^1(5(5(2(0(4(4(5(5(0(3(5(2(1(2(1(0(2(2(3(x1)))))))))))))))))))) -> 3^1(5(0(3(4(5(2(4(3(x1))))))))) 11.64/3.88 3^1(5(5(2(0(4(4(5(5(0(3(5(2(1(2(1(0(2(2(3(x1)))))))))))))))))))) -> 0^1(3(4(5(2(4(3(x1))))))) 11.64/3.88 3^1(5(5(2(0(4(4(5(5(0(3(5(2(1(2(1(0(2(2(3(x1)))))))))))))))))))) -> 3^1(4(5(2(4(3(x1)))))) 11.64/3.88 3^1(5(5(2(0(4(4(5(5(0(3(5(2(1(2(1(0(2(2(3(x1)))))))))))))))))))) -> 4^1(5(2(4(3(x1))))) 11.64/3.88 3^1(5(5(2(0(4(4(5(5(0(3(5(2(1(2(1(0(2(2(3(x1)))))))))))))))))))) -> 2^1(4(3(x1))) 11.64/3.88 3^1(5(5(2(0(4(4(5(5(0(3(5(2(1(2(1(0(2(2(3(x1)))))))))))))))))))) -> 4^1(3(x1)) 11.64/3.88 11.64/3.88 The TRS R consists of the following rules: 11.64/3.88 11.64/3.88 2(3(3(2(5(x1))))) -> 3(5(4(5(5(x1))))) 11.64/3.88 4(0(2(3(1(4(4(x1))))))) -> 4(1(3(0(5(0(5(x1))))))) 11.64/3.88 0(2(2(2(3(4(3(3(3(x1))))))))) -> 0(5(4(0(5(3(5(5(3(x1))))))))) 11.64/3.88 1(2(2(1(2(3(2(4(4(0(0(3(2(x1))))))))))))) -> 4(4(4(3(2(0(1(3(1(2(2(4(5(x1))))))))))))) 11.64/3.88 2(2(3(3(0(2(0(2(5(0(5(5(5(1(0(3(1(x1))))))))))))))))) -> 5(5(5(2(0(2(5(0(0(4(3(2(1(4(3(3(1(x1))))))))))))))))) 11.64/3.88 2(5(5(1(2(3(5(0(3(0(0(3(3(1(0(1(3(2(x1)))))))))))))))))) -> 2(1(5(0(0(1(5(2(2(2(3(1(0(5(0(4(3(3(x1)))))))))))))))))) 11.64/3.88 3(2(3(4(1(2(5(5(0(1(2(3(4(0(5(1(4(4(5(4(x1)))))))))))))))))))) -> 3(2(0(1(5(0(1(5(5(1(2(3(0(2(4(2(5(2(2(4(x1)))))))))))))))))))) 11.64/3.88 3(5(5(2(0(4(4(5(5(0(3(5(2(1(2(1(0(2(2(3(x1)))))))))))))))))))) -> 3(1(3(3(0(5(4(2(4(1(2(3(5(0(3(4(5(2(4(3(x1)))))))))))))))))))) 11.64/3.88 11.64/3.88 Q is empty. 11.64/3.88 We have to consider all minimal (P,Q,R)-chains. 11.64/3.88 ---------------------------------------- 11.64/3.88 11.64/3.88 (5) DependencyGraphProof (EQUIVALENT) 11.64/3.88 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 80 less nodes. 11.64/3.88 ---------------------------------------- 11.64/3.88 11.64/3.88 (6) 11.64/3.88 TRUE 11.99/3.93 EOF