29.32/8.36 YES 30.10/8.51 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 30.10/8.51 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 30.10/8.51 30.10/8.51 30.10/8.51 Termination w.r.t. Q of the given QTRS could be proven: 30.10/8.51 30.10/8.51 (0) QTRS 30.10/8.51 (1) QTRS Reverse [EQUIVALENT, 0 ms] 30.10/8.51 (2) QTRS 30.10/8.51 (3) QTRSRoofMatchBoundsTAProof [EQUIVALENT, 1239 ms] 30.10/8.51 (4) YES 30.10/8.51 30.10/8.51 30.10/8.51 ---------------------------------------- 30.10/8.51 30.10/8.51 (0) 30.10/8.51 Obligation: 30.10/8.51 Q restricted rewrite system: 30.10/8.51 The TRS R consists of the following rules: 30.10/8.51 30.10/8.51 0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(x1)))))))))) 30.10/8.51 0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(0(1(2(x1))))))))))))) 30.10/8.51 0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(x1)))))))))))))))) 30.10/8.51 0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))))) 30.10/8.51 0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1)))))))))))))))))))))) 30.10/8.51 0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))))))))))) 30.10/8.51 0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1)))))))))))))))))))))))))))) 30.10/8.51 0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))))))))))))))))) 30.10/8.51 0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1)))))))))))))))))))))))))))))))))) 30.10/8.51 0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))))))))))))))))))))))) 30.10/8.51 0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1)))))))))))))))))))))))))))))))))))))))) 30.10/8.51 30.10/8.51 Q is empty. 30.10/8.51 30.10/8.51 ---------------------------------------- 30.10/8.51 30.10/8.51 (1) QTRS Reverse (EQUIVALENT) 30.10/8.51 We applied the QTRS Reverse Processor [REVERSE]. 30.10/8.51 ---------------------------------------- 30.10/8.51 30.10/8.51 (2) 30.10/8.51 Obligation: 30.10/8.51 Q restricted rewrite system: 30.10/8.51 The TRS R consists of the following rules: 30.10/8.51 30.10/8.51 1(2(1(0(x1)))) -> 2(1(0(2(1(0(1(1(2(1(x1)))))))))) 30.10/8.51 1(2(1(0(x1)))) -> 2(1(0(2(1(0(2(1(0(1(1(2(1(x1))))))))))))) 30.10/8.51 1(2(1(0(x1)))) -> 2(1(0(2(1(0(2(1(0(2(1(0(1(1(2(1(x1)))))))))))))))) 30.10/8.51 1(2(1(0(x1)))) -> 2(1(0(2(1(0(2(1(0(2(1(0(2(1(0(1(1(2(1(x1))))))))))))))))))) 30.10/8.51 1(2(1(0(x1)))) -> 2(1(0(2(1(0(2(1(0(2(1(0(2(1(0(2(1(0(1(1(2(1(x1)))))))))))))))))))))) 30.10/8.51 1(2(1(0(x1)))) -> 2(1(0(2(1(0(2(1(0(2(1(0(2(1(0(2(1(0(2(1(0(1(1(2(1(x1))))))))))))))))))))))))) 30.10/8.51 1(2(1(0(x1)))) -> 2(1(0(2(1(0(2(1(0(2(1(0(2(1(0(2(1(0(2(1(0(2(1(0(1(1(2(1(x1)))))))))))))))))))))))))))) 30.10/8.51 1(2(1(0(x1)))) -> 2(1(0(2(1(0(2(1(0(2(1(0(2(1(0(2(1(0(2(1(0(2(1(0(2(1(0(1(1(2(1(x1))))))))))))))))))))))))))))))) 30.10/8.51 1(2(1(0(x1)))) -> 2(1(0(2(1(0(2(1(0(2(1(0(2(1(0(2(1(0(2(1(0(2(1(0(2(1(0(2(1(0(1(1(2(1(x1)))))))))))))))))))))))))))))))))) 30.10/8.51 1(2(1(0(x1)))) -> 2(1(0(2(1(0(2(1(0(2(1(0(2(1(0(2(1(0(2(1(0(2(1(0(2(1(0(2(1(0(2(1(0(1(1(2(1(x1))))))))))))))))))))))))))))))))))))) 30.10/8.51 1(2(1(0(x1)))) -> 2(1(0(2(1(0(2(1(0(2(1(0(2(1(0(2(1(0(2(1(0(2(1(0(2(1(0(2(1(0(2(1(0(2(1(0(1(1(2(1(x1)))))))))))))))))))))))))))))))))))))))) 30.10/8.51 30.10/8.51 Q is empty. 30.10/8.51 30.10/8.51 ---------------------------------------- 30.10/8.51 30.10/8.51 (3) QTRSRoofMatchBoundsTAProof (EQUIVALENT) 30.10/8.51 The TRS R could be shown to be Match-Bounded [TAB_LEFTLINEAR,TAB_NONLEFTLINEAR] by 3. Therefore it terminates. 30.10/8.51 30.10/8.51 The compatible tree automaton used to show the Match-Boundedness is represented by: 30.10/8.51 final states : [0, 1, 2] 30.10/8.51 transitions: 30.10/8.51 10(0) -> 0 30.10/8.51 10(1) -> 0 30.10/8.51 10(2) -> 0 30.10/8.51 20(0) -> 1 30.10/8.51 20(1) -> 1 30.10/8.51 20(2) -> 1 30.10/8.51 00(0) -> 2 30.10/8.51 00(1) -> 2 30.10/8.51 00(2) -> 2 30.10/8.51 11(0) -> 10 30.10/8.51 21(10) -> 9 30.10/8.51 11(9) -> 8 30.10/8.51 11(8) -> 7 30.10/8.51 01(7) -> 6 30.10/8.51 11(6) -> 3 30.10/8.51 21(3) -> 5 30.10/8.51 01(5) -> 4 30.10/8.51 11(4) -> 3 30.10/8.51 21(3) -> 0 30.10/8.51 11(1) -> 10 30.10/8.51 11(2) -> 10 30.10/8.51 11(7) -> 10 30.10/8.51 11(5) -> 10 30.10/8.51 12(7) -> 18 30.10/8.51 22(18) -> 17 30.10/8.51 12(17) -> 16 30.10/8.51 12(16) -> 15 30.10/8.51 02(15) -> 14 30.10/8.51 12(14) -> 11 30.10/8.51 22(11) -> 13 30.10/8.51 02(13) -> 12 30.10/8.51 12(12) -> 11 30.10/8.51 22(11) -> 10 30.10/8.51 12(5) -> 18 30.10/8.51 12(15) -> 18 30.10/8.51 13(15) -> 26 30.10/8.51 23(26) -> 25 30.10/8.51 13(25) -> 24 30.10/8.51 13(24) -> 23 30.10/8.51 03(23) -> 22 30.10/8.51 13(22) -> 19 30.10/8.51 23(19) -> 21 30.10/8.51 03(21) -> 20 30.10/8.51 13(20) -> 19 30.10/8.51 23(19) -> 18 30.10/8.51 13(13) -> 26 30.10/8.51 5 -> 10 30.10/8.51 5 -> 8 30.10/8.51 13 -> 7 30.10/8.51 13 -> 18 30.10/8.51 21 -> 26 30.10/8.51 30.10/8.51 ---------------------------------------- 30.10/8.51 30.10/8.51 (4) 30.10/8.51 YES 30.10/8.56 EOF