details

property	value
status	complete
benchmark	05.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n075.star.cs.uiowa.edu
space	Bouchare_06

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	7.18612 seconds
cpu usage	24.0708
user time	22.8011
system time	1.26971
max virtual memory	8.1563652E7
max residence set size	3445676.0

stage attributes

key	value
starexec-result	YES

output

23.58/7.09 YES 23.58/7.10 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 23.58/7.10 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 23.58/7.10 23.58/7.10 23.58/7.10 Termination w.r.t. Q of the given QTRS could be proven: 23.58/7.10 23.58/7.10 (0) QTRS 23.58/7.10 (1) DependencyPairsProof [EQUIVALENT, 0 ms] 23.58/7.10 (2) QDP 23.58/7.10 (3) QDPOrderProof [EQUIVALENT, 120 ms] 23.58/7.10 (4) QDP 23.58/7.10 (5) QDPOrderProof [EQUIVALENT, 57 ms] 23.58/7.10 (6) QDP 23.58/7.10 (7) DependencyGraphProof [EQUIVALENT, 0 ms] 23.58/7.10 (8) TRUE 23.58/7.10 23.58/7.10 23.58/7.10 ---------------------------------------- 23.58/7.10 23.58/7.10 (0) 23.58/7.10 Obligation: 23.58/7.10 Q restricted rewrite system: 23.58/7.10 The TRS R consists of the following rules: 23.58/7.10 23.58/7.10 a(b(b(x1))) -> a(x1) 23.58/7.10 a(a(x1)) -> b(b(b(x1))) 23.58/7.10 b(b(a(x1))) -> a(b(a(x1))) 23.58/7.10 23.58/7.10 Q is empty. 23.58/7.10 23.58/7.10 ---------------------------------------- 23.58/7.10 23.58/7.10 (1) DependencyPairsProof (EQUIVALENT) 23.58/7.10 Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. 23.58/7.10 ---------------------------------------- 23.58/7.10 23.58/7.10 (2) 23.58/7.10 Obligation: 23.58/7.10 Q DP problem: 23.58/7.10 The TRS P consists of the following rules: 23.58/7.10 23.58/7.10 A(b(b(x1))) -> A(x1) 23.58/7.10 A(a(x1)) -> B(b(b(x1))) 23.58/7.10 A(a(x1)) -> B(b(x1)) 23.58/7.10 A(a(x1)) -> B(x1) 23.58/7.10 B(b(a(x1))) -> A(b(a(x1))) 23.58/7.10 23.58/7.10 The TRS R consists of the following rules: 23.58/7.10 23.58/7.10 a(b(b(x1))) -> a(x1) 23.58/7.10 a(a(x1)) -> b(b(b(x1))) 23.58/7.10 b(b(a(x1))) -> a(b(a(x1))) 23.58/7.10 23.58/7.10 Q is empty. 23.58/7.10 We have to consider all minimal (P,Q,R)-chains. 23.58/7.10 ---------------------------------------- 23.58/7.10 23.58/7.10 (3) QDPOrderProof (EQUIVALENT) 23.58/7.10 We use the reduction pair processor [LPAR04,JAR06]. 23.58/7.10 23.58/7.10 23.58/7.10 The following pairs can be oriented strictly and are deleted. 23.58/7.10 23.58/7.10 A(b(b(x1))) -> A(x1) 23.58/7.10 The remaining pairs can at least be oriented weakly. 23.58/7.10 Used ordering: Matrix interpretation [MATRO] with arctic natural numbers [ARCTIC]: 23.58/7.10 23.58/7.10 <<< 23.58/7.10 POL(A(x_1)) = [[-I]] + [[0A, -I, 0A]] * x_1 23.58/7.10 >>> 23.58/7.10 23.58/7.10 <<< 23.58/7.10 POL(b(x_1)) = [[0A], [0A], [-I]] + [[0A, 0A, 1A], [-I, 0A, 0A], [0A, -I, 0A]] * x_1 23.58/7.10 >>> 23.58/7.10 23.58/7.10 <<< 23.58/7.10 POL(a(x_1)) = [[0A], [0A], [-I]] + [[1A, 0A, 1A], [0A, 0A, 0A], [0A, -I, 0A]] * x_1 23.58/7.10 >>> 23.58/7.10 23.58/7.10 <<< 23.58/7.10 POL(B(x_1)) = [[0A]] + [[-I, 0A, 0A]] * x_1 23.58/7.10 >>> 23.58/7.10 23.58/7.10 23.58/7.10 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 23.58/7.10 23.58/7.10 a(a(x1)) -> b(b(b(x1))) 23.58/7.10 b(b(a(x1))) -> a(b(a(x1))) 23.58/7.10 a(b(b(x1))) -> a(x1) 23.58/7.10 23.58/7.10 23.58/7.10 ---------------------------------------- 23.58/7.10 23.58/7.10 (4) 23.58/7.10 Obligation: 23.58/7.10 Q DP problem: 23.58/7.10 The TRS P consists of the following rules: 23.58/7.10 23.58/7.10 A(a(x1)) -> B(b(b(x1))) popout

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