details

property	value
status	complete
benchmark	size-12-alpha-3-num-477.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n083.star.cs.uiowa.edu
space	Waldmann_07_size12

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	7.93103 seconds
cpu usage	27.8013
user time	26.7583
system time	1.04303
max virtual memory	1.19091736E8
max residence set size	2528532.0

stage attributes

key	value
starexec-result	YES

output

27.67/7.87 YES 27.67/7.88 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 27.67/7.88 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 27.67/7.88 27.67/7.88 27.67/7.88 Termination w.r.t. Q of the given QTRS could be proven: 27.67/7.88 27.67/7.88 (0) QTRS 27.67/7.88 (1) DependencyPairsProof [EQUIVALENT, 22 ms] 27.67/7.88 (2) QDP 27.67/7.88 (3) DependencyGraphProof [EQUIVALENT, 0 ms] 27.67/7.88 (4) QDP 27.67/7.88 (5) QDPOrderProof [EQUIVALENT, 110 ms] 27.67/7.88 (6) QDP 27.67/7.88 (7) DependencyGraphProof [EQUIVALENT, 0 ms] 27.67/7.88 (8) QDP 27.67/7.88 (9) UsableRulesProof [EQUIVALENT, 0 ms] 27.67/7.88 (10) QDP 27.67/7.88 (11) QDPSizeChangeProof [EQUIVALENT, 0 ms] 27.67/7.88 (12) YES 27.67/7.88 27.67/7.88 27.67/7.88 ---------------------------------------- 27.67/7.88 27.67/7.88 (0) 27.67/7.88 Obligation: 27.67/7.88 Q restricted rewrite system: 27.67/7.88 The TRS R consists of the following rules: 27.67/7.88 27.67/7.88 a(a(x1)) -> a(b(b(c(x1)))) 27.67/7.88 a(b(x1)) -> x1 27.67/7.88 c(b(x1)) -> a(c(x1)) 27.67/7.88 27.67/7.88 Q is empty. 27.67/7.88 27.67/7.88 ---------------------------------------- 27.67/7.88 27.67/7.88 (1) DependencyPairsProof (EQUIVALENT) 27.67/7.88 Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. 27.67/7.88 ---------------------------------------- 27.67/7.88 27.67/7.88 (2) 27.67/7.88 Obligation: 27.67/7.88 Q DP problem: 27.67/7.88 The TRS P consists of the following rules: 27.67/7.88 27.67/7.88 A(a(x1)) -> A(b(b(c(x1)))) 27.67/7.88 A(a(x1)) -> C(x1) 27.67/7.88 C(b(x1)) -> A(c(x1)) 27.67/7.88 C(b(x1)) -> C(x1) 27.67/7.88 27.67/7.88 The TRS R consists of the following rules: 27.67/7.88 27.67/7.88 a(a(x1)) -> a(b(b(c(x1)))) 27.67/7.88 a(b(x1)) -> x1 27.67/7.88 c(b(x1)) -> a(c(x1)) 27.67/7.88 27.67/7.88 Q is empty. 27.67/7.88 We have to consider all minimal (P,Q,R)-chains. 27.67/7.88 ---------------------------------------- 27.67/7.88 27.67/7.88 (3) DependencyGraphProof (EQUIVALENT) 27.67/7.88 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 27.67/7.88 ---------------------------------------- 27.67/7.88 27.67/7.88 (4) 27.67/7.88 Obligation: 27.67/7.88 Q DP problem: 27.67/7.88 The TRS P consists of the following rules: 27.67/7.88 27.67/7.88 A(a(x1)) -> C(x1) 27.67/7.88 C(b(x1)) -> A(c(x1)) 27.67/7.88 C(b(x1)) -> C(x1) 27.67/7.88 27.67/7.88 The TRS R consists of the following rules: 27.67/7.88 27.67/7.88 a(a(x1)) -> a(b(b(c(x1)))) 27.67/7.88 a(b(x1)) -> x1 27.67/7.88 c(b(x1)) -> a(c(x1)) 27.67/7.88 27.67/7.88 Q is empty. 27.67/7.88 We have to consider all minimal (P,Q,R)-chains. 27.67/7.88 ---------------------------------------- 27.67/7.88 27.67/7.88 (5) QDPOrderProof (EQUIVALENT) 27.67/7.88 We use the reduction pair processor [LPAR04,JAR06]. 27.67/7.88 27.67/7.88 27.67/7.88 The following pairs can be oriented strictly and are deleted. 27.67/7.88 27.67/7.88 A(a(x1)) -> C(x1) 27.67/7.88 The remaining pairs can at least be oriented weakly. 27.67/7.88 Used ordering: Matrix interpretation [MATRO] with arctic natural numbers [ARCTIC]: 27.67/7.88 27.67/7.88 <<< 27.67/7.88 POL(A(x_1)) = [[0A]] + [[-I, 0A, 0A]] * x_1 27.67/7.88 >>> 27.67/7.88 27.67/7.88 <<< 27.67/7.88 POL(a(x_1)) = [[-I], [1A], [-I]] + [[0A, 0A, -I], [0A, 1A, 0A], [-I, 0A, -I]] * x_1 popout

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all output return to SRS_Standard 2019-03-29 03.29