details

property	value
status	complete
benchmark	size-12-alpha-3-num-341.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	Waldmann_07_size12

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	7.07322 seconds
cpu usage	24.3006
user time	23.0977
system time	1.2029
max virtual memory	2.0682668E7
max residence set size	3173420.0

stage attributes

key	value
starexec-result	YES

output

24.09/6.98 YES 24.09/6.99 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 24.09/6.99 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 24.09/6.99 24.09/6.99 24.09/6.99 Termination w.r.t. Q of the given QTRS could be proven: 24.09/6.99 24.09/6.99 (0) QTRS 24.09/6.99 (1) DependencyPairsProof [EQUIVALENT, 5 ms] 24.09/6.99 (2) QDP 24.09/6.99 (3) DependencyGraphProof [EQUIVALENT, 1 ms] 24.09/6.99 (4) QDP 24.09/6.99 (5) QDPOrderProof [EQUIVALENT, 157 ms] 24.09/6.99 (6) QDP 24.09/6.99 (7) UsableRulesProof [EQUIVALENT, 0 ms] 24.09/6.99 (8) QDP 24.09/6.99 (9) QDPSizeChangeProof [EQUIVALENT, 0 ms] 24.09/6.99 (10) YES 24.09/6.99 24.09/6.99 24.09/6.99 ---------------------------------------- 24.09/6.99 24.09/6.99 (0) 24.09/6.99 Obligation: 24.09/6.99 Q restricted rewrite system: 24.09/6.99 The TRS R consists of the following rules: 24.09/6.99 24.09/6.99 a(x1) -> b(x1) 24.09/6.99 a(a(c(x1))) -> c(a(c(a(a(x1))))) 24.09/6.99 c(c(x1)) -> x1 24.09/6.99 24.09/6.99 Q is empty. 24.09/6.99 24.09/6.99 ---------------------------------------- 24.09/6.99 24.09/6.99 (1) DependencyPairsProof (EQUIVALENT) 24.09/6.99 Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. 24.09/6.99 ---------------------------------------- 24.09/6.99 24.09/6.99 (2) 24.09/6.99 Obligation: 24.09/6.99 Q DP problem: 24.09/6.99 The TRS P consists of the following rules: 24.09/6.99 24.09/6.99 A(a(c(x1))) -> C(a(c(a(a(x1))))) 24.09/6.99 A(a(c(x1))) -> A(c(a(a(x1)))) 24.09/6.99 A(a(c(x1))) -> C(a(a(x1))) 24.09/6.99 A(a(c(x1))) -> A(a(x1)) 24.09/6.99 A(a(c(x1))) -> A(x1) 24.09/6.99 24.09/6.99 The TRS R consists of the following rules: 24.09/6.99 24.09/6.99 a(x1) -> b(x1) 24.09/6.99 a(a(c(x1))) -> c(a(c(a(a(x1))))) 24.09/6.99 c(c(x1)) -> x1 24.09/6.99 24.09/6.99 Q is empty. 24.09/6.99 We have to consider all minimal (P,Q,R)-chains. 24.09/6.99 ---------------------------------------- 24.09/6.99 24.09/6.99 (3) DependencyGraphProof (EQUIVALENT) 24.09/6.99 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. 24.09/6.99 ---------------------------------------- 24.09/6.99 24.09/6.99 (4) 24.09/6.99 Obligation: 24.09/6.99 Q DP problem: 24.09/6.99 The TRS P consists of the following rules: 24.09/6.99 24.09/6.99 A(a(c(x1))) -> A(a(x1)) 24.09/6.99 A(a(c(x1))) -> A(c(a(a(x1)))) 24.09/6.99 A(a(c(x1))) -> A(x1) 24.09/6.99 24.09/6.99 The TRS R consists of the following rules: 24.09/6.99 24.09/6.99 a(x1) -> b(x1) 24.09/6.99 a(a(c(x1))) -> c(a(c(a(a(x1))))) 24.09/6.99 c(c(x1)) -> x1 24.09/6.99 24.09/6.99 Q is empty. 24.09/6.99 We have to consider all minimal (P,Q,R)-chains. 24.09/6.99 ---------------------------------------- 24.09/6.99 24.09/6.99 (5) QDPOrderProof (EQUIVALENT) 24.09/6.99 We use the reduction pair processor [LPAR04,JAR06]. 24.09/6.99 24.09/6.99 24.09/6.99 The following pairs can be oriented strictly and are deleted. 24.09/6.99 24.09/6.99 A(a(c(x1))) -> A(a(x1)) 24.09/6.99 A(a(c(x1))) -> A(c(a(a(x1)))) 24.09/6.99 The remaining pairs can at least be oriented weakly. 24.09/6.99 Used ordering: Matrix interpretation [MATRO] with arctic natural numbers [ARCTIC]: 24.09/6.99 24.09/6.99 <<< 24.09/6.99 POL(A(x_1)) = [[0A]] + [[0A, 0A, 1A]] * x_1 24.09/6.99 >>> 24.09/6.99 24.09/6.99 <<< 24.09/6.99 POL(a(x_1)) = [[0A], [0A], [0A]] + [[-I, -I, 0A], [-I, -I, 0A], [0A, -I, -I]] * x_1 popout

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all output return to SRS_Standard 2019-03-29 03.29