details

property	value
status	complete
benchmark	size-12-alpha-3-num-347.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n130.star.cs.uiowa.edu
space	Waldmann_07_size12

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	8.10664 seconds
cpu usage	28.7104
user time	27.2101
system time	1.50034
max virtual memory	6.0078824E7
max residence set size	3949972.0

stage attributes

key	value
starexec-result	YES

output

27.94/7.95 YES 28.40/8.00 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 28.40/8.00 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 28.40/8.00 28.40/8.00 28.40/8.00 Termination w.r.t. Q of the given QTRS could be proven: 28.40/8.00 28.40/8.00 (0) QTRS 28.40/8.00 (1) DependencyPairsProof [EQUIVALENT, 0 ms] 28.40/8.00 (2) QDP 28.40/8.00 (3) DependencyGraphProof [EQUIVALENT, 6 ms] 28.40/8.00 (4) QDP 28.40/8.00 (5) QDPOrderProof [EQUIVALENT, 123 ms] 28.40/8.00 (6) QDP 28.40/8.00 (7) UsableRulesProof [EQUIVALENT, 0 ms] 28.40/8.00 (8) QDP 28.40/8.00 (9) QDPSizeChangeProof [EQUIVALENT, 0 ms] 28.40/8.00 (10) YES 28.40/8.00 28.40/8.00 28.40/8.00 ---------------------------------------- 28.40/8.00 28.40/8.00 (0) 28.40/8.00 Obligation: 28.40/8.00 Q restricted rewrite system: 28.40/8.00 The TRS R consists of the following rules: 28.40/8.00 28.40/8.00 a(x1) -> b(x1) 28.40/8.00 a(b(x1)) -> x1 28.40/8.00 c(c(b(x1))) -> a(c(a(c(c(x1))))) 28.40/8.00 28.40/8.00 Q is empty. 28.40/8.00 28.40/8.00 ---------------------------------------- 28.40/8.00 28.40/8.00 (1) DependencyPairsProof (EQUIVALENT) 28.40/8.00 Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. 28.40/8.00 ---------------------------------------- 28.40/8.00 28.40/8.00 (2) 28.40/8.00 Obligation: 28.40/8.00 Q DP problem: 28.40/8.00 The TRS P consists of the following rules: 28.40/8.00 28.40/8.00 C(c(b(x1))) -> A(c(a(c(c(x1))))) 28.40/8.00 C(c(b(x1))) -> C(a(c(c(x1)))) 28.40/8.00 C(c(b(x1))) -> A(c(c(x1))) 28.40/8.00 C(c(b(x1))) -> C(c(x1)) 28.40/8.00 C(c(b(x1))) -> C(x1) 28.40/8.00 28.40/8.00 The TRS R consists of the following rules: 28.40/8.00 28.40/8.00 a(x1) -> b(x1) 28.40/8.00 a(b(x1)) -> x1 28.40/8.00 c(c(b(x1))) -> a(c(a(c(c(x1))))) 28.40/8.00 28.40/8.00 Q is empty. 28.40/8.00 We have to consider all minimal (P,Q,R)-chains. 28.40/8.00 ---------------------------------------- 28.40/8.00 28.40/8.00 (3) DependencyGraphProof (EQUIVALENT) 28.40/8.00 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. 28.40/8.00 ---------------------------------------- 28.40/8.00 28.40/8.00 (4) 28.40/8.00 Obligation: 28.40/8.00 Q DP problem: 28.40/8.00 The TRS P consists of the following rules: 28.40/8.00 28.40/8.00 C(c(b(x1))) -> C(c(x1)) 28.40/8.00 C(c(b(x1))) -> C(a(c(c(x1)))) 28.40/8.00 C(c(b(x1))) -> C(x1) 28.40/8.00 28.40/8.00 The TRS R consists of the following rules: 28.40/8.00 28.40/8.00 a(x1) -> b(x1) 28.40/8.00 a(b(x1)) -> x1 28.40/8.00 c(c(b(x1))) -> a(c(a(c(c(x1))))) 28.40/8.00 28.40/8.00 Q is empty. 28.40/8.00 We have to consider all minimal (P,Q,R)-chains. 28.40/8.00 ---------------------------------------- 28.40/8.00 28.40/8.00 (5) QDPOrderProof (EQUIVALENT) 28.40/8.00 We use the reduction pair processor [LPAR04,JAR06]. 28.40/8.00 28.40/8.00 28.40/8.00 The following pairs can be oriented strictly and are deleted. 28.40/8.00 28.40/8.00 C(c(b(x1))) -> C(c(x1)) 28.40/8.00 C(c(b(x1))) -> C(a(c(c(x1)))) 28.40/8.00 The remaining pairs can at least be oriented weakly. 28.40/8.00 Used ordering: Matrix interpretation [MATRO] with arctic natural numbers [ARCTIC]: 28.40/8.00 28.40/8.00 <<< 28.40/8.00 POL(C(x_1)) = [[-I]] + [[0A, -I, 0A]] * x_1 28.40/8.00 >>> 28.40/8.00 28.40/8.00 <<< 28.40/8.00 POL(c(x_1)) = [[-I], [-I], [-I]] + [[0A, -I, -I], [0A, -I, 0A], [0A, 0A, -I]] * x_1 popout

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all output return to SRS_Standard 2019-03-29 03.29