details

property	value
status	complete
benchmark	z035.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n119.star.cs.uiowa.edu
space	Zantema_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.38488 seconds
cpu usage	4.16568
user time	4.00561
system time	0.160073
max virtual memory	1.914132E7
max residence set size	340456.0

stage attributes

key	value
starexec-result	YES

output

3.99/1.83 YES 3.99/1.84 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 3.99/1.84 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 3.99/1.84 3.99/1.84 3.99/1.84 Termination w.r.t. Q of the given QTRS could be proven: 3.99/1.84 3.99/1.84 (0) QTRS 3.99/1.84 (1) QTRS Reverse [EQUIVALENT, 0 ms] 3.99/1.84 (2) QTRS 3.99/1.84 (3) Strip Symbols Proof [SOUND, 0 ms] 3.99/1.84 (4) QTRS 3.99/1.84 (5) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms] 3.99/1.84 (6) YES 3.99/1.84 3.99/1.84 3.99/1.84 ---------------------------------------- 3.99/1.84 3.99/1.84 (0) 3.99/1.84 Obligation: 3.99/1.84 Q restricted rewrite system: 3.99/1.84 The TRS R consists of the following rules: 3.99/1.84 3.99/1.84 a(a(b(b(a(b(x1)))))) -> a(b(b(a(a(b(b(a(x1)))))))) 3.99/1.84 3.99/1.84 Q is empty. 3.99/1.84 3.99/1.84 ---------------------------------------- 3.99/1.84 3.99/1.84 (1) QTRS Reverse (EQUIVALENT) 3.99/1.84 We applied the QTRS Reverse Processor [REVERSE]. 3.99/1.84 ---------------------------------------- 3.99/1.84 3.99/1.84 (2) 3.99/1.84 Obligation: 3.99/1.84 Q restricted rewrite system: 3.99/1.84 The TRS R consists of the following rules: 3.99/1.84 3.99/1.84 b(a(b(b(a(a(x1)))))) -> a(b(b(a(a(b(b(a(x1)))))))) 3.99/1.84 3.99/1.84 Q is empty. 3.99/1.84 3.99/1.84 ---------------------------------------- 3.99/1.84 3.99/1.84 (3) Strip Symbols Proof (SOUND) 3.99/1.84 We were given the following TRS: 3.99/1.84 3.99/1.84 b(a(b(b(a(a(x1)))))) -> a(b(b(a(a(b(b(a(x1)))))))) 3.99/1.84 3.99/1.84 By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: 3.99/1.84 3.99/1.84 b(a(b(b(a(x))))) -> a(b(b(a(a(b(b(x))))))) 3.99/1.84 3.99/1.84 ---------------------------------------- 3.99/1.84 3.99/1.84 (4) 3.99/1.84 Obligation: 3.99/1.84 Q restricted rewrite system: 3.99/1.84 The TRS R consists of the following rules: 3.99/1.84 3.99/1.84 b(a(b(b(a(x))))) -> a(b(b(a(a(b(b(x))))))) 3.99/1.84 3.99/1.84 Q is empty. 3.99/1.84 3.99/1.84 ---------------------------------------- 3.99/1.84 3.99/1.84 (5) RFCMatchBoundsTRSProof (EQUIVALENT) 3.99/1.84 Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 2. This implies Q-termination of R. 3.99/1.84 The following rules were used to construct the certificate: 3.99/1.84 3.99/1.84 b(a(b(b(a(x))))) -> a(b(b(a(a(b(b(x))))))) 3.99/1.84 3.99/1.84 The certificate found is represented by the following graph. 3.99/1.84 The certificate consists of the following enumerated nodes: 3.99/1.84 343, 344, 345, 346, 347, 348, 349, 350, 351, 352, 353, 354, 355, 356, 357, 358, 359, 360, 361, 362, 363, 364, 365, 366, 367, 368 3.99/1.84 3.99/1.84 Node 343 is start node and node 344 is final node. 3.99/1.84 3.99/1.84 Those nodes are connected through the following edges: 3.99/1.84 3.99/1.84 * 343 to 345 labelled a_1(0)* 344 to 344 labelled #_1(0)* 345 to 346 labelled b_1(0)* 346 to 347 labelled b_1(0)* 347 to 348 labelled a_1(0)* 348 to 349 labelled a_1(0)* 349 to 350 labelled b_1(0)* 349 to 357 labelled a_1(1)* 350 to 344 labelled b_1(0)* 350 to 351 labelled a_1(1)* 351 to 352 labelled b_1(1)* 352 to 353 labelled b_1(1)* 353 to 354 labelled a_1(1)* 354 to 355 labelled a_1(1)* 355 to 356 labelled b_1(1)* 355 to 363 labelled a_1(2)* 356 to 344 labelled b_1(1)* 356 to 351 labelled a_1(1)* 357 to 358 labelled b_1(1)* 358 to 359 labelled b_1(1)* 359 to 360 labelled a_1(1)* 360 to 361 labelled a_1(1)* 361 to 362 labelled b_1(1)* 361 to 363 labelled a_1(2)* 362 to 354 labelled b_1(1)* 362 to 351 labelled a_1(1)* 363 to 364 labelled b_1(2)* 364 to 365 labelled b_1(2)* 365 to 366 labelled a_1(2)* 366 to 367 labelled a_1(2)* 367 to 368 labelled b_1(2)* 367 to 363 labelled a_1(2)* 368 to 354 labelled b_1(2)* 368 to 351 labelled a_1(1) 3.99/1.84 3.99/1.84 3.99/1.84 ---------------------------------------- 3.99/1.84 3.99/1.84 (6) 3.99/1.84 YES 4.14/2.38 EOF popout

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