9.19/3.14 YES 9.47/3.21 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 9.47/3.21 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 9.47/3.21 9.47/3.21 9.47/3.21 Termination w.r.t. Q of the given QTRS could be proven: 9.47/3.21 9.47/3.21 (0) QTRS 9.47/3.21 (1) QTRSRRRProof [EQUIVALENT, 142 ms] 9.47/3.21 (2) QTRS 9.47/3.21 (3) DependencyPairsProof [EQUIVALENT, 45 ms] 9.47/3.21 (4) QDP 9.47/3.21 (5) DependencyGraphProof [EQUIVALENT, 0 ms] 9.47/3.21 (6) TRUE 9.47/3.21 9.47/3.21 9.47/3.21 ---------------------------------------- 9.47/3.21 9.47/3.21 (0) 9.47/3.21 Obligation: 9.47/3.21 Q restricted rewrite system: 9.47/3.21 The TRS R consists of the following rules: 9.47/3.21 9.47/3.21 0(1(2(x1))) -> 1(3(2(x1))) 9.47/3.21 1(1(4(2(3(x1))))) -> 1(5(4(4(x1)))) 9.47/3.21 2(2(1(3(5(x1))))) -> 1(2(0(5(x1)))) 9.47/3.21 3(0(0(2(1(x1))))) -> 0(5(4(0(x1)))) 9.47/3.21 4(3(2(5(0(x1))))) -> 3(4(1(5(5(x1))))) 9.47/3.21 0(0(0(3(2(5(x1)))))) -> 2(0(5(5(4(5(x1)))))) 9.47/3.21 2(2(1(1(3(2(x1)))))) -> 2(1(4(0(0(x1))))) 9.47/3.21 3(3(1(1(2(2(x1)))))) -> 3(3(0(0(2(x1))))) 9.47/3.21 0(2(5(1(0(4(2(2(x1)))))))) -> 0(0(3(5(1(5(4(x1))))))) 9.47/3.21 4(0(5(3(5(1(3(5(x1)))))))) -> 4(0(0(1(3(0(1(5(x1)))))))) 9.47/3.21 4(4(4(3(5(1(4(0(x1)))))))) -> 3(0(2(2(2(2(3(2(x1)))))))) 9.47/3.21 0(0(5(3(2(2(5(0(3(x1))))))))) -> 2(5(5(4(2(2(5(0(3(x1))))))))) 9.47/3.21 3(2(2(0(0(0(0(3(1(0(5(x1))))))))))) -> 0(4(3(0(4(4(2(4(1(4(0(5(x1)))))))))))) 9.47/3.21 4(3(3(3(5(0(0(3(2(4(4(1(2(x1))))))))))))) -> 4(4(5(2(2(0(5(0(1(4(3(0(x1)))))))))))) 9.47/3.21 4(4(3(3(1(2(2(5(3(5(3(2(3(x1))))))))))))) -> 4(1(4(0(0(2(5(4(4(2(0(3(x1)))))))))))) 9.47/3.21 0(0(5(0(1(4(4(3(5(2(0(0(3(3(x1)))))))))))))) -> 2(1(2(1(2(0(4(0(2(2(4(3(3(5(4(x1))))))))))))))) 9.47/3.21 3(0(1(5(5(1(0(4(0(0(2(1(0(3(x1)))))))))))))) -> 3(4(0(1(2(5(2(2(0(3(0(4(5(1(x1)))))))))))))) 9.47/3.21 5(5(0(5(4(4(4(3(4(0(5(4(3(3(x1)))))))))))))) -> 2(4(5(0(2(0(3(0(2(5(3(1(3(3(x1)))))))))))))) 9.47/3.21 1(0(4(3(2(1(1(1(2(4(4(5(5(0(1(x1))))))))))))))) -> 1(0(2(4(5(5(0(1(1(4(4(5(0(1(x1)))))))))))))) 9.47/3.21 3(4(1(1(4(4(0(4(4(2(4(1(0(0(5(3(2(x1))))))))))))))))) -> 3(5(5(5(0(1(3(2(4(2(0(3(5(3(0(x1))))))))))))))) 9.47/3.21 0(2(1(3(5(3(4(1(1(4(4(0(4(3(4(1(0(2(x1)))))))))))))))))) -> 1(5(2(2(0(3(2(3(4(2(0(1(1(1(3(2(1(x1))))))))))))))))) 9.47/3.21 3(3(0(0(1(2(3(5(3(0(5(2(0(0(2(4(4(1(x1)))))))))))))))))) -> 2(2(4(1(4(4(2(5(2(2(5(1(4(2(5(2(0(4(1(x1))))))))))))))))))) 9.47/3.21 3(3(0(5(2(3(1(3(0(0(3(1(5(2(2(1(2(2(x1)))))))))))))))))) -> 1(0(3(0(4(2(4(3(2(0(4(2(1(5(5(2(2(x1))))))))))))))))) 9.47/3.21 4(5(4(0(1(1(5(5(4(5(3(2(1(3(2(4(4(2(x1)))))))))))))))))) -> 3(4(5(5(3(0(4(3(3(3(0(5(3(2(2(5(0(x1))))))))))))))))) 9.47/3.21 0(0(4(1(2(3(3(5(5(2(0(3(1(2(2(4(0(1(5(x1))))))))))))))))))) -> 2(2(0(1(0(1(5(0(1(0(0(5(0(1(1(4(5(x1))))))))))))))))) 9.47/3.21 0(5(0(3(2(3(2(3(0(1(5(5(5(3(4(0(0(2(2(x1))))))))))))))))))) -> 2(2(5(4(0(0(1(5(5(3(2(2(5(0(0(5(4(0(x1)))))))))))))))))) 9.47/3.21 4(0(3(4(1(3(2(0(0(0(2(1(0(1(1(3(1(5(1(x1))))))))))))))))))) -> 0(3(5(3(4(5(1(0(0(3(1(0(2(4(1(3(3(0(x1)))))))))))))))))) 9.47/3.21 4(4(5(4(5(4(3(1(2(2(0(2(5(4(2(0(4(1(2(x1))))))))))))))))))) -> 0(3(5(5(2(0(3(4(2(4(5(0(2(1(3(2(2(1(x1)))))))))))))))))) 9.47/3.21 3(3(3(5(2(0(0(3(3(1(2(5(2(1(3(1(0(5(2(2(x1)))))))))))))))))))) -> 3(4(5(0(5(3(1(3(5(5(5(4(0(4(1(2(5(5(0(x1))))))))))))))))))) 9.47/3.21 2(5(4(3(4(4(4(4(2(1(2(2(1(5(5(2(5(0(1(1(1(x1))))))))))))))))))))) -> 5(4(5(4(1(3(4(3(0(3(3(1(1(4(4(2(1(2(0(1(0(x1))))))))))))))))))))) 9.47/3.21 9.47/3.21 Q is empty. 9.47/3.21 9.47/3.21 ---------------------------------------- 9.47/3.21 9.47/3.21 (1) QTRSRRRProof (EQUIVALENT) 9.47/3.21 Used ordering: 9.47/3.21 Polynomial interpretation [POLO]: 9.47/3.21 9.47/3.21 POL(0(x_1)) = 17 + x_1 9.47/3.21 POL(1(x_1)) = 13 + x_1 9.47/3.21 POL(2(x_1)) = 13 + x_1 9.47/3.21 POL(3(x_1)) = 13 + x_1 9.47/3.21 POL(4(x_1)) = 12 + x_1 9.47/3.21 POL(5(x_1)) = 17 + x_1 9.47/3.21 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: 9.47/3.21 9.47/3.21 0(1(2(x1))) -> 1(3(2(x1))) 9.47/3.21 1(1(4(2(3(x1))))) -> 1(5(4(4(x1)))) 9.47/3.21 2(2(1(3(5(x1))))) -> 1(2(0(5(x1)))) 9.47/3.21 3(0(0(2(1(x1))))) -> 0(5(4(0(x1)))) 9.47/3.21 0(0(0(3(2(5(x1)))))) -> 2(0(5(5(4(5(x1)))))) 9.47/3.21 2(2(1(1(3(2(x1)))))) -> 2(1(4(0(0(x1))))) 9.47/3.21 3(3(1(1(2(2(x1)))))) -> 3(3(0(0(2(x1))))) 9.47/3.21 0(2(5(1(0(4(2(2(x1)))))))) -> 0(0(3(5(1(5(4(x1))))))) 9.47/3.21 0(0(5(3(2(2(5(0(3(x1))))))))) -> 2(5(5(4(2(2(5(0(3(x1))))))))) 9.47/3.21 4(3(3(3(5(0(0(3(2(4(4(1(2(x1))))))))))))) -> 4(4(5(2(2(0(5(0(1(4(3(0(x1)))))))))))) 9.47/3.21 4(4(3(3(1(2(2(5(3(5(3(2(3(x1))))))))))))) -> 4(1(4(0(0(2(5(4(4(2(0(3(x1)))))))))))) 9.47/3.21 0(0(5(0(1(4(4(3(5(2(0(0(3(3(x1)))))))))))))) -> 2(1(2(1(2(0(4(0(2(2(4(3(3(5(4(x1))))))))))))))) 9.47/3.21 3(0(1(5(5(1(0(4(0(0(2(1(0(3(x1)))))))))))))) -> 3(4(0(1(2(5(2(2(0(3(0(4(5(1(x1)))))))))))))) 9.47/3.21 1(0(4(3(2(1(1(1(2(4(4(5(5(0(1(x1))))))))))))))) -> 1(0(2(4(5(5(0(1(1(4(4(5(0(1(x1)))))))))))))) 9.47/3.21 3(4(1(1(4(4(0(4(4(2(4(1(0(0(5(3(2(x1))))))))))))))))) -> 3(5(5(5(0(1(3(2(4(2(0(3(5(3(0(x1))))))))))))))) 9.47/3.21 0(2(1(3(5(3(4(1(1(4(4(0(4(3(4(1(0(2(x1)))))))))))))))))) -> 1(5(2(2(0(3(2(3(4(2(0(1(1(1(3(2(1(x1))))))))))))))))) 9.47/3.21 3(3(0(0(1(2(3(5(3(0(5(2(0(0(2(4(4(1(x1)))))))))))))))))) -> 2(2(4(1(4(4(2(5(2(2(5(1(4(2(5(2(0(4(1(x1))))))))))))))))))) 9.47/3.21 3(3(0(5(2(3(1(3(0(0(3(1(5(2(2(1(2(2(x1)))))))))))))))))) -> 1(0(3(0(4(2(4(3(2(0(4(2(1(5(5(2(2(x1))))))))))))))))) 9.47/3.21 4(5(4(0(1(1(5(5(4(5(3(2(1(3(2(4(4(2(x1)))))))))))))))))) -> 3(4(5(5(3(0(4(3(3(3(0(5(3(2(2(5(0(x1))))))))))))))))) 9.47/3.21 0(0(4(1(2(3(3(5(5(2(0(3(1(2(2(4(0(1(5(x1))))))))))))))))))) -> 2(2(0(1(0(1(5(0(1(0(0(5(0(1(1(4(5(x1))))))))))))))))) 9.47/3.21 0(5(0(3(2(3(2(3(0(1(5(5(5(3(4(0(0(2(2(x1))))))))))))))))))) -> 2(2(5(4(0(0(1(5(5(3(2(2(5(0(0(5(4(0(x1)))))))))))))))))) 9.47/3.21 4(0(3(4(1(3(2(0(0(0(2(1(0(1(1(3(1(5(1(x1))))))))))))))))))) -> 0(3(5(3(4(5(1(0(0(3(1(0(2(4(1(3(3(0(x1)))))))))))))))))) 9.47/3.21 4(4(5(4(5(4(3(1(2(2(0(2(5(4(2(0(4(1(2(x1))))))))))))))))))) -> 0(3(5(5(2(0(3(4(2(4(5(0(2(1(3(2(2(1(x1)))))))))))))))))) 9.47/3.21 9.47/3.21 9.47/3.21 9.47/3.21 9.47/3.21 ---------------------------------------- 9.47/3.21 9.47/3.21 (2) 9.47/3.21 Obligation: 9.47/3.21 Q restricted rewrite system: 9.47/3.21 The TRS R consists of the following rules: 9.47/3.21 9.47/3.21 4(3(2(5(0(x1))))) -> 3(4(1(5(5(x1))))) 9.47/3.21 4(0(5(3(5(1(3(5(x1)))))))) -> 4(0(0(1(3(0(1(5(x1)))))))) 9.47/3.21 4(4(4(3(5(1(4(0(x1)))))))) -> 3(0(2(2(2(2(3(2(x1)))))))) 9.47/3.21 3(2(2(0(0(0(0(3(1(0(5(x1))))))))))) -> 0(4(3(0(4(4(2(4(1(4(0(5(x1)))))))))))) 9.47/3.21 5(5(0(5(4(4(4(3(4(0(5(4(3(3(x1)))))))))))))) -> 2(4(5(0(2(0(3(0(2(5(3(1(3(3(x1)))))))))))))) 9.47/3.21 3(3(3(5(2(0(0(3(3(1(2(5(2(1(3(1(0(5(2(2(x1)))))))))))))))))))) -> 3(4(5(0(5(3(1(3(5(5(5(4(0(4(1(2(5(5(0(x1))))))))))))))))))) 9.47/3.21 2(5(4(3(4(4(4(4(2(1(2(2(1(5(5(2(5(0(1(1(1(x1))))))))))))))))))))) -> 5(4(5(4(1(3(4(3(0(3(3(1(1(4(4(2(1(2(0(1(0(x1))))))))))))))))))))) 9.47/3.21 9.47/3.21 Q is empty. 9.47/3.21 9.47/3.21 ---------------------------------------- 9.47/3.21 9.47/3.21 (3) DependencyPairsProof (EQUIVALENT) 9.47/3.21 Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. 9.47/3.21 ---------------------------------------- 9.47/3.21 9.47/3.21 (4) 9.47/3.21 Obligation: 9.47/3.21 Q DP problem: 9.47/3.21 The TRS P consists of the following rules: 9.47/3.21 9.47/3.21 4^1(3(2(5(0(x1))))) -> 3^1(4(1(5(5(x1))))) 9.47/3.21 4^1(3(2(5(0(x1))))) -> 4^1(1(5(5(x1)))) 9.47/3.21 4^1(3(2(5(0(x1))))) -> 5^1(5(x1)) 9.47/3.21 4^1(3(2(5(0(x1))))) -> 5^1(x1) 9.47/3.21 4^1(0(5(3(5(1(3(5(x1)))))))) -> 4^1(0(0(1(3(0(1(5(x1)))))))) 9.47/3.21 4^1(0(5(3(5(1(3(5(x1)))))))) -> 3^1(0(1(5(x1)))) 9.47/3.21 4^1(4(4(3(5(1(4(0(x1)))))))) -> 3^1(0(2(2(2(2(3(2(x1)))))))) 9.47/3.21 4^1(4(4(3(5(1(4(0(x1)))))))) -> 2^1(2(2(2(3(2(x1)))))) 9.47/3.21 4^1(4(4(3(5(1(4(0(x1)))))))) -> 2^1(2(2(3(2(x1))))) 9.47/3.21 4^1(4(4(3(5(1(4(0(x1)))))))) -> 2^1(2(3(2(x1)))) 9.47/3.21 4^1(4(4(3(5(1(4(0(x1)))))))) -> 2^1(3(2(x1))) 9.47/3.21 4^1(4(4(3(5(1(4(0(x1)))))))) -> 3^1(2(x1)) 9.47/3.21 4^1(4(4(3(5(1(4(0(x1)))))))) -> 2^1(x1) 9.47/3.21 3^1(2(2(0(0(0(0(3(1(0(5(x1))))))))))) -> 4^1(3(0(4(4(2(4(1(4(0(5(x1))))))))))) 9.47/3.21 3^1(2(2(0(0(0(0(3(1(0(5(x1))))))))))) -> 3^1(0(4(4(2(4(1(4(0(5(x1)))))))))) 9.47/3.21 3^1(2(2(0(0(0(0(3(1(0(5(x1))))))))))) -> 4^1(4(2(4(1(4(0(5(x1)))))))) 9.47/3.21 3^1(2(2(0(0(0(0(3(1(0(5(x1))))))))))) -> 4^1(2(4(1(4(0(5(x1))))))) 9.47/3.21 3^1(2(2(0(0(0(0(3(1(0(5(x1))))))))))) -> 2^1(4(1(4(0(5(x1)))))) 9.47/3.21 3^1(2(2(0(0(0(0(3(1(0(5(x1))))))))))) -> 4^1(1(4(0(5(x1))))) 9.47/3.21 3^1(2(2(0(0(0(0(3(1(0(5(x1))))))))))) -> 4^1(0(5(x1))) 9.47/3.21 5^1(5(0(5(4(4(4(3(4(0(5(4(3(3(x1)))))))))))))) -> 2^1(4(5(0(2(0(3(0(2(5(3(1(3(3(x1)))))))))))))) 9.47/3.21 5^1(5(0(5(4(4(4(3(4(0(5(4(3(3(x1)))))))))))))) -> 4^1(5(0(2(0(3(0(2(5(3(1(3(3(x1))))))))))))) 9.47/3.21 5^1(5(0(5(4(4(4(3(4(0(5(4(3(3(x1)))))))))))))) -> 5^1(0(2(0(3(0(2(5(3(1(3(3(x1)))))))))))) 9.47/3.21 5^1(5(0(5(4(4(4(3(4(0(5(4(3(3(x1)))))))))))))) -> 2^1(0(3(0(2(5(3(1(3(3(x1)))))))))) 9.47/3.21 5^1(5(0(5(4(4(4(3(4(0(5(4(3(3(x1)))))))))))))) -> 3^1(0(2(5(3(1(3(3(x1)))))))) 9.47/3.21 5^1(5(0(5(4(4(4(3(4(0(5(4(3(3(x1)))))))))))))) -> 2^1(5(3(1(3(3(x1)))))) 9.47/3.21 5^1(5(0(5(4(4(4(3(4(0(5(4(3(3(x1)))))))))))))) -> 5^1(3(1(3(3(x1))))) 9.47/3.21 5^1(5(0(5(4(4(4(3(4(0(5(4(3(3(x1)))))))))))))) -> 3^1(1(3(3(x1)))) 9.47/3.21 3^1(3(3(5(2(0(0(3(3(1(2(5(2(1(3(1(0(5(2(2(x1)))))))))))))))))))) -> 3^1(4(5(0(5(3(1(3(5(5(5(4(0(4(1(2(5(5(0(x1))))))))))))))))))) 9.47/3.21 3^1(3(3(5(2(0(0(3(3(1(2(5(2(1(3(1(0(5(2(2(x1)))))))))))))))))))) -> 4^1(5(0(5(3(1(3(5(5(5(4(0(4(1(2(5(5(0(x1)))))))))))))))))) 9.47/3.21 3^1(3(3(5(2(0(0(3(3(1(2(5(2(1(3(1(0(5(2(2(x1)))))))))))))))))))) -> 5^1(0(5(3(1(3(5(5(5(4(0(4(1(2(5(5(0(x1))))))))))))))))) 9.47/3.21 3^1(3(3(5(2(0(0(3(3(1(2(5(2(1(3(1(0(5(2(2(x1)))))))))))))))))))) -> 5^1(3(1(3(5(5(5(4(0(4(1(2(5(5(0(x1))))))))))))))) 9.47/3.21 3^1(3(3(5(2(0(0(3(3(1(2(5(2(1(3(1(0(5(2(2(x1)))))))))))))))))))) -> 3^1(1(3(5(5(5(4(0(4(1(2(5(5(0(x1)))))))))))))) 9.47/3.21 3^1(3(3(5(2(0(0(3(3(1(2(5(2(1(3(1(0(5(2(2(x1)))))))))))))))))))) -> 3^1(5(5(5(4(0(4(1(2(5(5(0(x1)))))))))))) 9.47/3.21 3^1(3(3(5(2(0(0(3(3(1(2(5(2(1(3(1(0(5(2(2(x1)))))))))))))))))))) -> 5^1(5(5(4(0(4(1(2(5(5(0(x1))))))))))) 9.47/3.21 3^1(3(3(5(2(0(0(3(3(1(2(5(2(1(3(1(0(5(2(2(x1)))))))))))))))))))) -> 5^1(5(4(0(4(1(2(5(5(0(x1)))))))))) 9.47/3.21 3^1(3(3(5(2(0(0(3(3(1(2(5(2(1(3(1(0(5(2(2(x1)))))))))))))))))))) -> 5^1(4(0(4(1(2(5(5(0(x1))))))))) 9.47/3.21 3^1(3(3(5(2(0(0(3(3(1(2(5(2(1(3(1(0(5(2(2(x1)))))))))))))))))))) -> 4^1(0(4(1(2(5(5(0(x1)))))))) 9.47/3.21 3^1(3(3(5(2(0(0(3(3(1(2(5(2(1(3(1(0(5(2(2(x1)))))))))))))))))))) -> 4^1(1(2(5(5(0(x1)))))) 9.47/3.21 3^1(3(3(5(2(0(0(3(3(1(2(5(2(1(3(1(0(5(2(2(x1)))))))))))))))))))) -> 2^1(5(5(0(x1)))) 9.47/3.21 3^1(3(3(5(2(0(0(3(3(1(2(5(2(1(3(1(0(5(2(2(x1)))))))))))))))))))) -> 5^1(5(0(x1))) 9.47/3.21 3^1(3(3(5(2(0(0(3(3(1(2(5(2(1(3(1(0(5(2(2(x1)))))))))))))))))))) -> 5^1(0(x1)) 9.47/3.21 2^1(5(4(3(4(4(4(4(2(1(2(2(1(5(5(2(5(0(1(1(1(x1))))))))))))))))))))) -> 5^1(4(5(4(1(3(4(3(0(3(3(1(1(4(4(2(1(2(0(1(0(x1))))))))))))))))))))) 9.47/3.21 2^1(5(4(3(4(4(4(4(2(1(2(2(1(5(5(2(5(0(1(1(1(x1))))))))))))))))))))) -> 4^1(5(4(1(3(4(3(0(3(3(1(1(4(4(2(1(2(0(1(0(x1)))))))))))))))))))) 9.47/3.21 2^1(5(4(3(4(4(4(4(2(1(2(2(1(5(5(2(5(0(1(1(1(x1))))))))))))))))))))) -> 5^1(4(1(3(4(3(0(3(3(1(1(4(4(2(1(2(0(1(0(x1))))))))))))))))))) 9.47/3.21 2^1(5(4(3(4(4(4(4(2(1(2(2(1(5(5(2(5(0(1(1(1(x1))))))))))))))))))))) -> 4^1(1(3(4(3(0(3(3(1(1(4(4(2(1(2(0(1(0(x1)))))))))))))))))) 9.47/3.21 2^1(5(4(3(4(4(4(4(2(1(2(2(1(5(5(2(5(0(1(1(1(x1))))))))))))))))))))) -> 3^1(4(3(0(3(3(1(1(4(4(2(1(2(0(1(0(x1)))))))))))))))) 9.47/3.21 2^1(5(4(3(4(4(4(4(2(1(2(2(1(5(5(2(5(0(1(1(1(x1))))))))))))))))))))) -> 4^1(3(0(3(3(1(1(4(4(2(1(2(0(1(0(x1))))))))))))))) 9.47/3.21 2^1(5(4(3(4(4(4(4(2(1(2(2(1(5(5(2(5(0(1(1(1(x1))))))))))))))))))))) -> 3^1(0(3(3(1(1(4(4(2(1(2(0(1(0(x1)))))))))))))) 9.47/3.21 2^1(5(4(3(4(4(4(4(2(1(2(2(1(5(5(2(5(0(1(1(1(x1))))))))))))))))))))) -> 3^1(3(1(1(4(4(2(1(2(0(1(0(x1)))))))))))) 9.47/3.21 2^1(5(4(3(4(4(4(4(2(1(2(2(1(5(5(2(5(0(1(1(1(x1))))))))))))))))))))) -> 3^1(1(1(4(4(2(1(2(0(1(0(x1))))))))))) 9.47/3.21 2^1(5(4(3(4(4(4(4(2(1(2(2(1(5(5(2(5(0(1(1(1(x1))))))))))))))))))))) -> 4^1(4(2(1(2(0(1(0(x1)))))))) 9.47/3.21 2^1(5(4(3(4(4(4(4(2(1(2(2(1(5(5(2(5(0(1(1(1(x1))))))))))))))))))))) -> 4^1(2(1(2(0(1(0(x1))))))) 9.47/3.21 2^1(5(4(3(4(4(4(4(2(1(2(2(1(5(5(2(5(0(1(1(1(x1))))))))))))))))))))) -> 2^1(1(2(0(1(0(x1)))))) 9.47/3.21 2^1(5(4(3(4(4(4(4(2(1(2(2(1(5(5(2(5(0(1(1(1(x1))))))))))))))))))))) -> 2^1(0(1(0(x1)))) 9.47/3.21 9.47/3.21 The TRS R consists of the following rules: 9.47/3.21 9.47/3.21 4(3(2(5(0(x1))))) -> 3(4(1(5(5(x1))))) 9.47/3.21 4(0(5(3(5(1(3(5(x1)))))))) -> 4(0(0(1(3(0(1(5(x1)))))))) 9.47/3.21 4(4(4(3(5(1(4(0(x1)))))))) -> 3(0(2(2(2(2(3(2(x1)))))))) 9.47/3.21 3(2(2(0(0(0(0(3(1(0(5(x1))))))))))) -> 0(4(3(0(4(4(2(4(1(4(0(5(x1)))))))))))) 9.47/3.21 5(5(0(5(4(4(4(3(4(0(5(4(3(3(x1)))))))))))))) -> 2(4(5(0(2(0(3(0(2(5(3(1(3(3(x1)))))))))))))) 9.47/3.21 3(3(3(5(2(0(0(3(3(1(2(5(2(1(3(1(0(5(2(2(x1)))))))))))))))))))) -> 3(4(5(0(5(3(1(3(5(5(5(4(0(4(1(2(5(5(0(x1))))))))))))))))))) 9.47/3.21 2(5(4(3(4(4(4(4(2(1(2(2(1(5(5(2(5(0(1(1(1(x1))))))))))))))))))))) -> 5(4(5(4(1(3(4(3(0(3(3(1(1(4(4(2(1(2(0(1(0(x1))))))))))))))))))))) 9.47/3.21 9.47/3.21 Q is empty. 9.47/3.21 We have to consider all minimal (P,Q,R)-chains. 9.47/3.21 ---------------------------------------- 9.47/3.21 9.47/3.21 (5) DependencyGraphProof (EQUIVALENT) 9.47/3.21 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 55 less nodes. 9.47/3.21 ---------------------------------------- 9.47/3.21 9.47/3.21 (6) 9.47/3.21 TRUE 9.47/3.25 EOF