details

property	value
status	complete
benchmark	size-12-alpha-3-num-532.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n007.star.cs.uiowa.edu
space	Waldmann_07_size12

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	6.15628 seconds
cpu usage	20.5084
user time	19.468
system time	1.04041
max virtual memory	4.0436048E7
max residence set size	2852988.0

stage attributes

key	value
starexec-result	YES

output

20.18/6.07 YES 20.18/6.08 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 20.18/6.08 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 20.18/6.08 20.18/6.08 20.18/6.08 Termination w.r.t. Q of the given QTRS could be proven: 20.18/6.08 20.18/6.08 (0) QTRS 20.18/6.08 (1) QTRS Reverse [EQUIVALENT, 0 ms] 20.18/6.08 (2) QTRS 20.18/6.08 (3) DependencyPairsProof [EQUIVALENT, 5 ms] 20.18/6.08 (4) QDP 20.18/6.08 (5) QDPOrderProof [EQUIVALENT, 109 ms] 20.18/6.08 (6) QDP 20.18/6.08 (7) UsableRulesProof [EQUIVALENT, 0 ms] 20.18/6.08 (8) QDP 20.18/6.08 (9) QDPSizeChangeProof [EQUIVALENT, 0 ms] 20.18/6.08 (10) YES 20.18/6.08 20.18/6.08 20.18/6.08 ---------------------------------------- 20.18/6.08 20.18/6.08 (0) 20.18/6.08 Obligation: 20.18/6.08 Q restricted rewrite system: 20.18/6.08 The TRS R consists of the following rules: 20.18/6.08 20.18/6.08 a(a(b(x1))) -> c(x1) 20.18/6.08 a(c(x1)) -> b(c(a(a(x1)))) 20.18/6.08 b(c(x1)) -> x1 20.18/6.08 20.18/6.08 Q is empty. 20.18/6.08 20.18/6.08 ---------------------------------------- 20.18/6.08 20.18/6.08 (1) QTRS Reverse (EQUIVALENT) 20.18/6.08 We applied the QTRS Reverse Processor [REVERSE]. 20.18/6.08 ---------------------------------------- 20.18/6.08 20.18/6.08 (2) 20.18/6.08 Obligation: 20.18/6.08 Q restricted rewrite system: 20.18/6.08 The TRS R consists of the following rules: 20.18/6.08 20.18/6.08 b(a(a(x1))) -> c(x1) 20.18/6.08 c(a(x1)) -> a(a(c(b(x1)))) 20.18/6.08 c(b(x1)) -> x1 20.18/6.08 20.18/6.08 Q is empty. 20.18/6.08 20.18/6.08 ---------------------------------------- 20.18/6.08 20.18/6.08 (3) DependencyPairsProof (EQUIVALENT) 20.18/6.08 Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. 20.18/6.08 ---------------------------------------- 20.18/6.08 20.18/6.08 (4) 20.18/6.08 Obligation: 20.18/6.08 Q DP problem: 20.18/6.08 The TRS P consists of the following rules: 20.18/6.08 20.18/6.08 B(a(a(x1))) -> C(x1) 20.18/6.08 C(a(x1)) -> C(b(x1)) 20.18/6.08 C(a(x1)) -> B(x1) 20.18/6.08 20.18/6.08 The TRS R consists of the following rules: 20.18/6.08 20.18/6.08 b(a(a(x1))) -> c(x1) 20.18/6.08 c(a(x1)) -> a(a(c(b(x1)))) 20.18/6.08 c(b(x1)) -> x1 20.18/6.08 20.18/6.08 Q is empty. 20.18/6.08 We have to consider all minimal (P,Q,R)-chains. 20.18/6.08 ---------------------------------------- 20.18/6.08 20.18/6.08 (5) QDPOrderProof (EQUIVALENT) 20.18/6.08 We use the reduction pair processor [LPAR04,JAR06]. 20.18/6.08 20.18/6.08 20.18/6.08 The following pairs can be oriented strictly and are deleted. 20.18/6.08 20.18/6.08 C(a(x1)) -> C(b(x1)) 20.18/6.08 The remaining pairs can at least be oriented weakly. 20.18/6.08 Used ordering: Matrix interpretation [MATRO] with arctic natural numbers [ARCTIC]: 20.18/6.08 20.18/6.08 <<< 20.18/6.08 POL(B(x_1)) = [[0A]] + [[0A, -I, -I]] * x_1 20.18/6.08 >>> 20.18/6.08 20.18/6.08 <<< 20.18/6.08 POL(a(x_1)) = [[1A], [1A], [0A]] + [[-I, 0A, 1A], [1A, -I, 0A], [0A, -I, -I]] * x_1 20.18/6.08 >>> 20.18/6.08 20.18/6.08 <<< 20.18/6.08 POL(C(x_1)) = [[1A]] + [[1A, -I, 0A]] * x_1 20.18/6.08 >>> 20.18/6.08 20.18/6.08 <<< 20.18/6.08 POL(b(x_1)) = [[0A], [0A], [-I]] + [[-I, -I, 0A], [0A, -I, -I], [-I, 0A, 0A]] * x_1 20.18/6.08 >>> popout

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all output return to SRS_Standard 2019-03-29 03.29