details

property	value
status	complete
benchmark	7.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n132.star.cs.uiowa.edu
space	Secret_06_SRS

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	5.56317 seconds
cpu usage	18.2227
user time	17.4184
system time	0.804329
max virtual memory	2.0241032E7
max residence set size	2152972.0

stage attributes

key	value
starexec-result	YES

output

17.92/5.46 YES 17.98/5.49 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 17.98/5.49 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 17.98/5.49 17.98/5.49 17.98/5.49 Termination w.r.t. Q of the given QTRS could be proven: 17.98/5.49 17.98/5.49 (0) QTRS 17.98/5.49 (1) DependencyPairsProof [EQUIVALENT, 12 ms] 17.98/5.49 (2) QDP 17.98/5.49 (3) QDPOrderProof [EQUIVALENT, 120 ms] 17.98/5.49 (4) QDP 17.98/5.49 (5) UsableRulesProof [EQUIVALENT, 0 ms] 17.98/5.49 (6) QDP 17.98/5.49 (7) QDPSizeChangeProof [EQUIVALENT, 0 ms] 17.98/5.49 (8) YES 17.98/5.49 17.98/5.49 17.98/5.49 ---------------------------------------- 17.98/5.49 17.98/5.49 (0) 17.98/5.49 Obligation: 17.98/5.49 Q restricted rewrite system: 17.98/5.49 The TRS R consists of the following rules: 17.98/5.49 17.98/5.49 a(b(b(x1))) -> b(a(a(a(x1)))) 17.98/5.49 a(a(b(x1))) -> b(a(b(x1))) 17.98/5.49 17.98/5.49 Q is empty. 17.98/5.49 17.98/5.49 ---------------------------------------- 17.98/5.49 17.98/5.49 (1) DependencyPairsProof (EQUIVALENT) 17.98/5.49 Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. 17.98/5.49 ---------------------------------------- 17.98/5.49 17.98/5.49 (2) 17.98/5.49 Obligation: 17.98/5.49 Q DP problem: 17.98/5.49 The TRS P consists of the following rules: 17.98/5.49 17.98/5.49 A(b(b(x1))) -> A(a(a(x1))) 17.98/5.49 A(b(b(x1))) -> A(a(x1)) 17.98/5.49 A(b(b(x1))) -> A(x1) 17.98/5.49 17.98/5.49 The TRS R consists of the following rules: 17.98/5.49 17.98/5.49 a(b(b(x1))) -> b(a(a(a(x1)))) 17.98/5.49 a(a(b(x1))) -> b(a(b(x1))) 17.98/5.49 17.98/5.49 Q is empty. 17.98/5.49 We have to consider all minimal (P,Q,R)-chains. 17.98/5.49 ---------------------------------------- 17.98/5.49 17.98/5.49 (3) QDPOrderProof (EQUIVALENT) 17.98/5.49 We use the reduction pair processor [LPAR04,JAR06]. 17.98/5.49 17.98/5.49 17.98/5.49 The following pairs can be oriented strictly and are deleted. 17.98/5.49 17.98/5.49 A(b(b(x1))) -> A(a(a(x1))) 17.98/5.49 A(b(b(x1))) -> A(a(x1)) 17.98/5.49 The remaining pairs can at least be oriented weakly. 17.98/5.49 Used ordering: Matrix interpretation [MATRO] with arctic natural numbers [ARCTIC]: 17.98/5.49 17.98/5.49 <<< 17.98/5.49 POL(A(x_1)) = [[0A]] + [[0A, 0A, -I]] * x_1 17.98/5.49 >>> 17.98/5.49 17.98/5.49 <<< 17.98/5.49 POL(b(x_1)) = [[0A], [1A], [-I]] + [[-I, -I, -I], [-I, -I, 0A], [0A, 1A, -I]] * x_1 17.98/5.49 >>> 17.98/5.49 17.98/5.49 <<< 17.98/5.49 POL(a(x_1)) = [[0A], [-I], [0A]] + [[-I, 0A, -I], [-I, 0A, -I], [1A, 0A, -I]] * x_1 17.98/5.49 >>> 17.98/5.49 17.98/5.49 17.98/5.49 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 17.98/5.49 17.98/5.49 a(b(b(x1))) -> b(a(a(a(x1)))) 17.98/5.49 a(a(b(x1))) -> b(a(b(x1))) 17.98/5.49 17.98/5.49 17.98/5.49 ---------------------------------------- 17.98/5.49 17.98/5.49 (4) 17.98/5.49 Obligation: 17.98/5.49 Q DP problem: 17.98/5.49 The TRS P consists of the following rules: 17.98/5.49 17.98/5.49 A(b(b(x1))) -> A(x1) 17.98/5.49 17.98/5.49 The TRS R consists of the following rules: 17.98/5.49 17.98/5.49 a(b(b(x1))) -> b(a(a(a(x1)))) 17.98/5.49 a(a(b(x1))) -> b(a(b(x1))) 17.98/5.49 17.98/5.49 Q is empty. 17.98/5.49 We have to consider all minimal (P,Q,R)-chains. popout

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