details

property	value
status	complete
benchmark	13.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n048.star.cs.uiowa.edu
space	Bouchare_06

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	10.8612 seconds
cpu usage	25.4691
user time	24.3065
system time	1.16262
max virtual memory	6.2024484E7
max residence set size	3411160.0

stage attributes

key	value
starexec-result	YES

output

25.24/7.32 YES 25.29/7.32 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 25.29/7.32 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 25.29/7.32 25.29/7.32 25.29/7.32 Termination w.r.t. Q of the given QTRS could be proven: 25.29/7.32 25.29/7.32 (0) QTRS 25.29/7.32 (1) DependencyPairsProof [EQUIVALENT, 6 ms] 25.29/7.32 (2) QDP 25.29/7.32 (3) QDPOrderProof [EQUIVALENT, 152 ms] 25.29/7.32 (4) QDP 25.29/7.32 (5) QDPOrderProof [EQUIVALENT, 0 ms] 25.29/7.32 (6) QDP 25.29/7.32 (7) DependencyGraphProof [EQUIVALENT, 0 ms] 25.29/7.32 (8) TRUE 25.29/7.32 25.29/7.32 25.29/7.32 ---------------------------------------- 25.29/7.32 25.29/7.32 (0) 25.29/7.32 Obligation: 25.29/7.32 Q restricted rewrite system: 25.29/7.32 The TRS R consists of the following rules: 25.29/7.32 25.29/7.32 a(a(b(x1))) -> a(x1) 25.29/7.32 a(b(a(x1))) -> b(b(a(x1))) 25.29/7.32 b(b(x1)) -> a(a(a(x1))) 25.29/7.32 25.29/7.32 Q is empty. 25.29/7.32 25.29/7.32 ---------------------------------------- 25.29/7.32 25.29/7.32 (1) DependencyPairsProof (EQUIVALENT) 25.29/7.32 Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. 25.29/7.32 ---------------------------------------- 25.29/7.32 25.29/7.32 (2) 25.29/7.32 Obligation: 25.29/7.32 Q DP problem: 25.29/7.32 The TRS P consists of the following rules: 25.29/7.32 25.29/7.32 A(a(b(x1))) -> A(x1) 25.29/7.32 A(b(a(x1))) -> B(b(a(x1))) 25.29/7.32 B(b(x1)) -> A(a(a(x1))) 25.29/7.32 B(b(x1)) -> A(a(x1)) 25.29/7.32 B(b(x1)) -> A(x1) 25.29/7.32 25.29/7.32 The TRS R consists of the following rules: 25.29/7.32 25.29/7.32 a(a(b(x1))) -> a(x1) 25.29/7.32 a(b(a(x1))) -> b(b(a(x1))) 25.29/7.32 b(b(x1)) -> a(a(a(x1))) 25.29/7.32 25.29/7.32 Q is empty. 25.29/7.32 We have to consider all minimal (P,Q,R)-chains. 25.29/7.32 ---------------------------------------- 25.29/7.32 25.29/7.32 (3) QDPOrderProof (EQUIVALENT) 25.29/7.32 We use the reduction pair processor [LPAR04,JAR06]. 25.29/7.32 25.29/7.32 25.29/7.32 The following pairs can be oriented strictly and are deleted. 25.29/7.32 25.29/7.32 A(a(b(x1))) -> A(x1) 25.29/7.32 The remaining pairs can at least be oriented weakly. 25.29/7.32 Used ordering: Matrix interpretation [MATRO] with arctic natural numbers [ARCTIC]: 25.29/7.32 25.29/7.32 <<< 25.29/7.32 POL(A(x_1)) = [[0A]] + [[-I, 0A, 0A]] * x_1 25.29/7.32 >>> 25.29/7.32 25.29/7.32 <<< 25.29/7.32 POL(a(x_1)) = [[-I], [0A], [-I]] + [[0A, -I, -I], [0A, 0A, 0A], [1A, 0A, 0A]] * x_1 25.29/7.32 >>> 25.29/7.32 25.29/7.32 <<< 25.29/7.32 POL(b(x_1)) = [[0A], [-I], [-I]] + [[0A, 0A, 0A], [0A, -I, 0A], [1A, -I, 0A]] * x_1 25.29/7.32 >>> 25.29/7.32 25.29/7.32 <<< 25.29/7.32 POL(B(x_1)) = [[-I]] + [[0A, 0A, 0A]] * x_1 25.29/7.32 >>> 25.29/7.32 25.29/7.32 25.29/7.32 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 25.29/7.32 25.29/7.32 a(b(a(x1))) -> b(b(a(x1))) 25.29/7.32 b(b(x1)) -> a(a(a(x1))) 25.29/7.32 a(a(b(x1))) -> a(x1) 25.29/7.32 25.29/7.32 25.29/7.32 ---------------------------------------- 25.29/7.32 25.29/7.32 (4) 25.29/7.32 Obligation: 25.29/7.32 Q DP problem: 25.29/7.32 The TRS P consists of the following rules: 25.29/7.32 25.29/7.32 A(b(a(x1))) -> B(b(a(x1))) popout

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