details

property	value
status	complete
benchmark	size-12-alpha-2-num-13.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n177.star.cs.uiowa.edu
space	Waldmann_07_size12

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	7.75268 seconds
cpu usage	26.6963
user time	25.4328
system time	1.26342
max virtual memory	2.104034E7
max residence set size	3629620.0

stage attributes

key	value
starexec-result	YES

output

26.33/7.64 YES 26.33/7.68 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 26.33/7.68 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 26.33/7.68 26.33/7.68 26.33/7.68 Termination w.r.t. Q of the given QTRS could be proven: 26.33/7.68 26.33/7.68 (0) QTRS 26.33/7.68 (1) QTRS Reverse [EQUIVALENT, 0 ms] 26.33/7.68 (2) QTRS 26.33/7.68 (3) DependencyPairsProof [EQUIVALENT, 0 ms] 26.33/7.68 (4) QDP 26.33/7.68 (5) QDPOrderProof [EQUIVALENT, 207 ms] 26.33/7.68 (6) QDP 26.33/7.68 (7) QDPOrderProof [EQUIVALENT, 0 ms] 26.33/7.68 (8) QDP 26.33/7.68 (9) PisEmptyProof [EQUIVALENT, 0 ms] 26.33/7.68 (10) YES 26.33/7.68 26.33/7.68 26.33/7.68 ---------------------------------------- 26.33/7.68 26.33/7.68 (0) 26.33/7.68 Obligation: 26.33/7.68 Q restricted rewrite system: 26.33/7.68 The TRS R consists of the following rules: 26.33/7.68 26.33/7.68 a(a(a(b(x1)))) -> b(a(b(a(a(a(x1)))))) 26.33/7.68 a(b(x1)) -> x1 26.33/7.68 26.33/7.68 Q is empty. 26.33/7.68 26.33/7.68 ---------------------------------------- 26.33/7.68 26.33/7.68 (1) QTRS Reverse (EQUIVALENT) 26.33/7.68 We applied the QTRS Reverse Processor [REVERSE]. 26.33/7.68 ---------------------------------------- 26.33/7.68 26.33/7.68 (2) 26.33/7.68 Obligation: 26.33/7.68 Q restricted rewrite system: 26.33/7.68 The TRS R consists of the following rules: 26.33/7.68 26.33/7.68 b(a(a(a(x1)))) -> a(a(a(b(a(b(x1)))))) 26.33/7.68 b(a(x1)) -> x1 26.33/7.68 26.33/7.68 Q is empty. 26.33/7.68 26.33/7.68 ---------------------------------------- 26.33/7.68 26.33/7.68 (3) DependencyPairsProof (EQUIVALENT) 26.33/7.68 Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. 26.33/7.68 ---------------------------------------- 26.33/7.68 26.33/7.68 (4) 26.33/7.68 Obligation: 26.33/7.68 Q DP problem: 26.33/7.68 The TRS P consists of the following rules: 26.33/7.68 26.33/7.68 B(a(a(a(x1)))) -> B(a(b(x1))) 26.33/7.68 B(a(a(a(x1)))) -> B(x1) 26.33/7.68 26.33/7.68 The TRS R consists of the following rules: 26.33/7.68 26.33/7.68 b(a(a(a(x1)))) -> a(a(a(b(a(b(x1)))))) 26.33/7.68 b(a(x1)) -> x1 26.33/7.68 26.33/7.68 Q is empty. 26.33/7.68 We have to consider all minimal (P,Q,R)-chains. 26.33/7.68 ---------------------------------------- 26.33/7.68 26.33/7.68 (5) QDPOrderProof (EQUIVALENT) 26.33/7.68 We use the reduction pair processor [LPAR04,JAR06]. 26.33/7.68 26.33/7.68 26.33/7.68 The following pairs can be oriented strictly and are deleted. 26.33/7.68 26.33/7.68 B(a(a(a(x1)))) -> B(x1) 26.33/7.68 The remaining pairs can at least be oriented weakly. 26.33/7.68 Used ordering: Matrix interpretation [MATRO] with arctic natural numbers [ARCTIC]: 26.33/7.68 26.33/7.68 <<< 26.33/7.68 POL(B(x_1)) = [[0A]] + [[0A, 0A, 0A]] * x_1 26.33/7.68 >>> 26.33/7.68 26.33/7.68 <<< 26.33/7.68 POL(a(x_1)) = [[1A], [-I], [-I]] + [[-I, 1A, 0A], [-I, -I, 0A], [0A, 0A, -I]] * x_1 26.33/7.68 >>> 26.33/7.68 26.33/7.68 <<< 26.33/7.68 POL(b(x_1)) = [[0A], [-I], [-I]] + [[-I, -I, 0A], [-I, -I, 0A], [0A, 0A, 1A]] * x_1 26.33/7.68 >>> 26.33/7.68 26.33/7.68 26.33/7.68 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 26.33/7.68 26.33/7.68 b(a(a(a(x1)))) -> a(a(a(b(a(b(x1)))))) 26.33/7.68 b(a(x1)) -> x1 26.33/7.68 26.33/7.68 popout

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