details

property	value
status	complete
benchmark	un07.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n128.star.cs.uiowa.edu
space	Trafo_06

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	8.90471 seconds
cpu usage	30.7406
user time	29.3227
system time	1.41788
max virtual memory	3.9692568E7
max residence set size	4033312.0

stage attributes

key	value
starexec-result	YES

output

28.45/8.22 YES 30.45/8.81 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 30.45/8.81 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 30.45/8.81 30.45/8.81 30.45/8.81 Termination w.r.t. Q of the given QTRS could be proven: 30.45/8.81 30.45/8.81 (0) QTRS 30.45/8.81 (1) DependencyPairsProof [EQUIVALENT, 14 ms] 30.45/8.81 (2) QDP 30.45/8.81 (3) QDPOrderProof [EQUIVALENT, 552 ms] 30.45/8.81 (4) QDP 30.45/8.81 (5) DependencyGraphProof [EQUIVALENT, 0 ms] 30.45/8.81 (6) TRUE 30.45/8.81 30.45/8.81 30.45/8.81 ---------------------------------------- 30.45/8.81 30.45/8.81 (0) 30.45/8.81 Obligation: 30.45/8.81 Q restricted rewrite system: 30.45/8.81 The TRS R consists of the following rules: 30.45/8.81 30.45/8.81 b(b(x1)) -> b(a(b(x1))) 30.45/8.81 b(b(a(b(x1)))) -> b(a(b(a(a(b(b(x1))))))) 30.45/8.81 b(a(b(x1))) -> b(a(a(b(x1)))) 30.45/8.81 b(a(a(b(a(b(x1)))))) -> b(b(x1)) 30.45/8.81 30.45/8.81 Q is empty. 30.45/8.81 30.45/8.81 ---------------------------------------- 30.45/8.81 30.45/8.81 (1) DependencyPairsProof (EQUIVALENT) 30.45/8.81 Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. 30.45/8.81 ---------------------------------------- 30.45/8.81 30.45/8.81 (2) 30.45/8.81 Obligation: 30.45/8.81 Q DP problem: 30.45/8.81 The TRS P consists of the following rules: 30.45/8.81 30.45/8.81 B(b(x1)) -> B(a(b(x1))) 30.45/8.81 B(b(a(b(x1)))) -> B(a(b(a(a(b(b(x1))))))) 30.45/8.81 B(b(a(b(x1)))) -> B(a(a(b(b(x1))))) 30.45/8.81 B(b(a(b(x1)))) -> B(b(x1)) 30.45/8.81 B(a(b(x1))) -> B(a(a(b(x1)))) 30.45/8.81 B(a(a(b(a(b(x1)))))) -> B(b(x1)) 30.45/8.81 30.45/8.81 The TRS R consists of the following rules: 30.45/8.81 30.45/8.81 b(b(x1)) -> b(a(b(x1))) 30.45/8.81 b(b(a(b(x1)))) -> b(a(b(a(a(b(b(x1))))))) 30.45/8.81 b(a(b(x1))) -> b(a(a(b(x1)))) 30.45/8.81 b(a(a(b(a(b(x1)))))) -> b(b(x1)) 30.45/8.81 30.45/8.81 Q is empty. 30.45/8.81 We have to consider all minimal (P,Q,R)-chains. 30.45/8.81 ---------------------------------------- 30.45/8.81 30.45/8.81 (3) QDPOrderProof (EQUIVALENT) 30.45/8.81 We use the reduction pair processor [LPAR04,JAR06]. 30.45/8.81 30.45/8.81 30.45/8.81 The following pairs can be oriented strictly and are deleted. 30.45/8.81 30.45/8.81 B(b(a(b(x1)))) -> B(b(x1)) 30.45/8.81 B(a(a(b(a(b(x1)))))) -> B(b(x1)) 30.45/8.81 The remaining pairs can at least be oriented weakly. 30.45/8.81 Used ordering: Matrix interpretation [MATRO] with arctic natural numbers [ARCTIC]: 30.45/8.81 30.45/8.81 <<< 30.45/8.81 POL(B(x_1)) = [[-I]] + [[0A, 0A, 0A]] * x_1 30.45/8.81 >>> 30.45/8.81 30.45/8.81 <<< 30.45/8.81 POL(b(x_1)) = [[-I], [-I], [-I]] + [[0A, 0A, -I], [0A, 1A, 0A], [0A, 1A, 0A]] * x_1 30.45/8.81 >>> 30.45/8.81 30.45/8.81 <<< 30.45/8.81 POL(a(x_1)) = [[-I], [-I], [-I]] + [[0A, 0A, 0A], [-I, -I, 0A], [0A, -I, -I]] * x_1 30.45/8.81 >>> 30.45/8.81 30.45/8.81 30.45/8.81 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 30.45/8.81 30.45/8.81 b(a(b(x1))) -> b(a(a(b(x1)))) 30.45/8.81 b(a(a(b(a(b(x1)))))) -> b(b(x1)) 30.45/8.81 b(b(x1)) -> b(a(b(x1))) 30.45/8.81 b(b(a(b(x1)))) -> b(a(b(a(a(b(b(x1))))))) 30.45/8.81 30.45/8.81 30.45/8.81 ---------------------------------------- 30.45/8.81 30.45/8.81 (4) 30.45/8.81 Obligation: 30.45/8.81 Q DP problem: 30.45/8.81 The TRS P consists of the following rules: 30.45/8.81 30.45/8.81 B(b(x1)) -> B(a(b(x1))) 30.45/8.81 B(b(a(b(x1)))) -> B(a(b(a(a(b(b(x1))))))) popout

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all output return to SRS_Standard 2019-03-29 03.29