61.08/16.44 YES 63.07/16.92 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 63.07/16.92 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 63.07/16.92 63.07/16.92 63.07/16.92 Termination w.r.t. Q of the given QTRS could be proven: 63.07/16.92 63.07/16.92 (0) QTRS 63.07/16.92 (1) QTRS Reverse [EQUIVALENT, 0 ms] 63.07/16.92 (2) QTRS 63.07/16.92 (3) QTRSRoofMatchBoundsTAProof [EQUIVALENT, 2115 ms] 63.07/16.92 (4) YES 63.07/16.92 63.07/16.92 63.07/16.92 ---------------------------------------- 63.07/16.92 63.07/16.92 (0) 63.07/16.92 Obligation: 63.07/16.92 Q restricted rewrite system: 63.07/16.92 The TRS R consists of the following rules: 63.07/16.92 63.07/16.92 0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(x1)))))))))) 63.07/16.92 0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(0(1(2(x1))))))))))))) 63.07/16.92 0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(x1)))))))))))))))) 63.07/16.92 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))))))))))))))))))) 63.07/16.92 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)))))))))))))))))))))) 63.07/16.92 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))))))))))))))))))))))))) 63.07/16.92 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)))))))))))))))))))))))))))) 63.07/16.92 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))))))))))))))))))))))))))))))) 63.07/16.92 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)))))))))))))))))))))))))))))))))) 63.07/16.92 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))))))))))))))))))))))))))))))))))))) 63.07/16.92 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)))))))))))))))))))))))))))))))))))))))) 63.07/16.92 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(0(1(2(x1))))))))))))))))))))))))))))))))))))))))))) 63.07/16.92 63.07/16.92 Q is empty. 63.07/16.92 63.07/16.92 ---------------------------------------- 63.07/16.92 63.07/16.92 (1) QTRS Reverse (EQUIVALENT) 63.07/16.92 We applied the QTRS Reverse Processor [REVERSE]. 63.07/16.92 ---------------------------------------- 63.07/16.92 63.07/16.92 (2) 63.07/16.92 Obligation: 63.07/16.92 Q restricted rewrite system: 63.07/16.92 The TRS R consists of the following rules: 63.07/16.92 63.07/16.92 1(2(1(0(x1)))) -> 2(1(0(2(1(0(1(1(2(1(x1)))))))))) 63.07/16.92 1(2(1(0(x1)))) -> 2(1(0(2(1(0(2(1(0(1(1(2(1(x1))))))))))))) 63.07/16.92 1(2(1(0(x1)))) -> 2(1(0(2(1(0(2(1(0(2(1(0(1(1(2(1(x1)))))))))))))))) 63.07/16.92 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))))))))))))))))))) 63.07/16.92 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)))))))))))))))))))))) 63.07/16.92 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))))))))))))))))))))))))) 63.07/16.92 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)))))))))))))))))))))))))))) 63.07/16.92 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))))))))))))))))))))))))))))))) 63.07/16.92 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)))))))))))))))))))))))))))))))))) 63.07/16.92 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))))))))))))))))))))))))))))))))))))) 63.07/16.92 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)))))))))))))))))))))))))))))))))))))))) 63.07/16.92 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(2(1(0(1(1(2(1(x1))))))))))))))))))))))))))))))))))))))))))) 63.07/16.92 63.07/16.92 Q is empty. 63.07/16.92 63.07/16.92 ---------------------------------------- 63.07/16.92 63.07/16.92 (3) QTRSRoofMatchBoundsTAProof (EQUIVALENT) 63.07/16.92 The TRS R could be shown to be Match-Bounded [TAB_LEFTLINEAR,TAB_NONLEFTLINEAR] by 3. Therefore it terminates. 63.07/16.92 63.07/16.92 The compatible tree automaton used to show the Match-Boundedness is represented by: 63.07/16.92 final states : [0, 1, 2] 63.07/16.92 transitions: 63.07/16.92 10(0) -> 0 63.07/16.92 10(1) -> 0 63.07/16.92 10(2) -> 0 63.07/16.92 20(0) -> 1 63.07/16.92 20(1) -> 1 63.07/16.92 20(2) -> 1 63.07/16.92 00(0) -> 2 63.07/16.92 00(1) -> 2 63.07/16.92 00(2) -> 2 63.07/16.92 11(0) -> 10 63.07/16.92 21(10) -> 9 63.07/16.92 11(9) -> 8 63.07/16.92 11(8) -> 7 63.07/16.92 01(7) -> 6 63.07/16.92 11(6) -> 3 63.07/16.92 21(3) -> 5 63.07/16.92 01(5) -> 4 63.07/16.92 11(4) -> 3 63.07/16.92 21(3) -> 0 63.07/16.92 11(1) -> 10 63.07/16.92 11(2) -> 10 63.07/16.92 11(7) -> 10 63.07/16.92 11(5) -> 10 63.07/16.92 12(7) -> 18 63.07/16.92 22(18) -> 17 63.07/16.92 12(17) -> 16 63.07/16.92 12(16) -> 15 63.07/16.92 02(15) -> 14 63.07/16.92 12(14) -> 11 63.07/16.92 22(11) -> 13 63.07/16.92 02(13) -> 12 63.07/16.92 12(12) -> 11 63.07/16.92 22(11) -> 10 63.07/16.92 12(5) -> 18 63.07/16.92 12(15) -> 18 63.07/16.92 13(15) -> 26 63.07/16.92 23(26) -> 25 63.07/16.92 13(25) -> 24 63.07/16.92 13(24) -> 23 63.07/16.92 03(23) -> 22 63.07/16.92 13(22) -> 19 63.07/16.92 23(19) -> 21 63.07/16.92 03(21) -> 20 63.07/16.92 13(20) -> 19 63.07/16.92 23(19) -> 18 63.07/16.92 13(13) -> 26 63.07/16.92 5 -> 10 63.07/16.92 5 -> 8 63.07/16.92 13 -> 7 63.07/16.92 13 -> 18 63.07/16.92 21 -> 26 63.07/16.92 63.07/16.92 ---------------------------------------- 63.07/16.92 63.07/16.92 (4) 63.07/16.92 YES 63.47/17.14 EOF