3.74/1.74 YES 3.74/1.76 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 3.74/1.76 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 3.74/1.76 3.74/1.76 3.74/1.76 Termination w.r.t. Q of the given QTRS could be proven: 3.74/1.76 3.74/1.76 (0) QTRS 3.74/1.76 (1) QTRS Reverse [EQUIVALENT, 0 ms] 3.74/1.76 (2) QTRS 3.74/1.76 (3) Strip Symbols Proof [SOUND, 0 ms] 3.74/1.76 (4) QTRS 3.74/1.76 (5) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms] 3.74/1.76 (6) YES 3.74/1.76 3.74/1.76 3.74/1.76 ---------------------------------------- 3.74/1.76 3.74/1.76 (0) 3.74/1.76 Obligation: 3.74/1.76 Q restricted rewrite system: 3.74/1.76 The TRS R consists of the following rules: 3.74/1.76 3.74/1.76 a(b(b(a(a(b(a(x1))))))) -> a(b(a(a(b(b(a(a(b(x1))))))))) 3.74/1.76 3.74/1.76 Q is empty. 3.74/1.76 3.74/1.76 ---------------------------------------- 3.74/1.76 3.74/1.76 (1) QTRS Reverse (EQUIVALENT) 3.74/1.76 We applied the QTRS Reverse Processor [REVERSE]. 3.74/1.76 ---------------------------------------- 3.74/1.76 3.74/1.76 (2) 3.74/1.76 Obligation: 3.74/1.76 Q restricted rewrite system: 3.74/1.76 The TRS R consists of the following rules: 3.74/1.76 3.74/1.76 a(b(a(a(b(b(a(x1))))))) -> b(a(a(b(b(a(a(b(a(x1))))))))) 3.74/1.76 3.74/1.76 Q is empty. 3.74/1.76 3.74/1.76 ---------------------------------------- 3.74/1.76 3.74/1.76 (3) Strip Symbols Proof (SOUND) 3.74/1.76 We were given the following TRS: 3.74/1.76 3.74/1.76 a(b(a(a(b(b(a(x1))))))) -> b(a(a(b(b(a(a(b(a(x1))))))))) 3.74/1.76 3.74/1.76 By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: 3.74/1.76 3.74/1.76 a(b(a(a(b(b(x)))))) -> b(a(a(b(b(a(a(b(x)))))))) 3.74/1.76 3.74/1.76 ---------------------------------------- 3.74/1.76 3.74/1.76 (4) 3.74/1.76 Obligation: 3.74/1.76 Q restricted rewrite system: 3.74/1.76 The TRS R consists of the following rules: 3.74/1.76 3.74/1.76 a(b(a(a(b(b(x)))))) -> b(a(a(b(b(a(a(b(x)))))))) 3.74/1.76 3.74/1.76 Q is empty. 3.74/1.76 3.74/1.76 ---------------------------------------- 3.74/1.76 3.74/1.76 (5) RFCMatchBoundsTRSProof (EQUIVALENT) 3.74/1.76 Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 2. This implies Q-termination of R. 3.74/1.76 The following rules were used to construct the certificate: 3.74/1.76 3.74/1.76 a(b(a(a(b(b(x)))))) -> b(a(a(b(b(a(a(b(x)))))))) 3.74/1.76 3.74/1.76 The certificate found is represented by the following graph. 3.74/1.76 The certificate consists of the following enumerated nodes: 3.74/1.76 328, 329, 330, 331, 332, 333, 334, 335, 336, 337, 338, 339, 340, 341, 342, 343, 344, 345, 346, 347, 348, 349, 350, 351, 352, 353, 354, 355, 356, 357 3.74/1.76 3.74/1.76 Node 328 is start node and node 329 is final node. 3.74/1.76 3.74/1.76 Those nodes are connected through the following edges: 3.74/1.76 3.74/1.76 * 328 to 330 labelled b_1(0)* 329 to 329 labelled #_1(0)* 330 to 331 labelled a_1(0)* 331 to 332 labelled a_1(0)* 332 to 333 labelled b_1(0)* 333 to 334 labelled b_1(0)* 334 to 335 labelled a_1(0)* 334 to 344 labelled b_1(1)* 335 to 336 labelled a_1(0)* 335 to 337 labelled b_1(1)* 336 to 329 labelled b_1(0)* 337 to 338 labelled a_1(1)* 338 to 339 labelled a_1(1)* 339 to 340 labelled b_1(1)* 340 to 341 labelled b_1(1)* 341 to 342 labelled a_1(1)* 341 to 351 labelled b_1(2)* 342 to 343 labelled a_1(1)* 342 to 337 labelled b_1(1)* 343 to 329 labelled b_1(1)* 344 to 345 labelled a_1(1)* 345 to 346 labelled a_1(1)* 346 to 347 labelled b_1(1)* 347 to 348 labelled b_1(1)* 348 to 349 labelled a_1(1)* 348 to 351 labelled b_1(2)* 349 to 350 labelled a_1(1)* 349 to 337 labelled b_1(1)* 350 to 341 labelled b_1(1)* 351 to 352 labelled a_1(2)* 352 to 353 labelled a_1(2)* 353 to 354 labelled b_1(2)* 354 to 355 labelled b_1(2)* 355 to 356 labelled a_1(2)* 355 to 351 labelled b_1(2)* 356 to 357 labelled a_1(2)* 356 to 337 labelled b_1(1)* 357 to 341 labelled b_1(2) 3.74/1.76 3.74/1.76 3.74/1.76 ---------------------------------------- 3.74/1.76 3.74/1.76 (6) 3.74/1.76 YES 4.02/1.78 EOF