details

property	value
status	complete
benchmark	size-12-alpha-3-num-556.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n125.star.cs.uiowa.edu
space	Waldmann_07_size12

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	11.3446 seconds
cpu usage	40.8028
user time	39.0254
system time	1.77742
max virtual memory	4.1758432E7
max residence set size	4237188.0

stage attributes

key	value
starexec-result	YES

output

40.20/11.23 YES 40.61/11.26 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 40.61/11.26 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 40.61/11.26 40.61/11.26 40.61/11.26 Termination w.r.t. Q of the given QTRS could be proven: 40.61/11.26 40.61/11.26 (0) QTRS 40.61/11.26 (1) DependencyPairsProof [EQUIVALENT, 6 ms] 40.61/11.26 (2) QDP 40.61/11.26 (3) DependencyGraphProof [EQUIVALENT, 0 ms] 40.61/11.26 (4) QDP 40.61/11.26 (5) QDPOrderProof [EQUIVALENT, 47 ms] 40.61/11.26 (6) QDP 40.61/11.26 (7) QDPOrderProof [EQUIVALENT, 129 ms] 40.61/11.26 (8) QDP 40.61/11.26 (9) PisEmptyProof [EQUIVALENT, 0 ms] 40.61/11.26 (10) YES 40.61/11.26 40.61/11.26 40.61/11.26 ---------------------------------------- 40.61/11.26 40.61/11.26 (0) 40.61/11.26 Obligation: 40.61/11.26 Q restricted rewrite system: 40.61/11.26 The TRS R consists of the following rules: 40.61/11.26 40.61/11.26 a(b(x1)) -> x1 40.61/11.26 a(c(x1)) -> c(b(b(c(a(a(x1)))))) 40.61/11.26 b(c(x1)) -> x1 40.61/11.26 40.61/11.26 Q is empty. 40.61/11.26 40.61/11.26 ---------------------------------------- 40.61/11.26 40.61/11.26 (1) DependencyPairsProof (EQUIVALENT) 40.61/11.26 Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. 40.61/11.26 ---------------------------------------- 40.61/11.26 40.61/11.26 (2) 40.61/11.26 Obligation: 40.61/11.26 Q DP problem: 40.61/11.26 The TRS P consists of the following rules: 40.61/11.26 40.61/11.26 A(c(x1)) -> B(b(c(a(a(x1))))) 40.61/11.26 A(c(x1)) -> B(c(a(a(x1)))) 40.61/11.26 A(c(x1)) -> A(a(x1)) 40.61/11.26 A(c(x1)) -> A(x1) 40.61/11.26 40.61/11.26 The TRS R consists of the following rules: 40.61/11.26 40.61/11.26 a(b(x1)) -> x1 40.61/11.26 a(c(x1)) -> c(b(b(c(a(a(x1)))))) 40.61/11.26 b(c(x1)) -> x1 40.61/11.26 40.61/11.26 Q is empty. 40.61/11.26 We have to consider all minimal (P,Q,R)-chains. 40.61/11.26 ---------------------------------------- 40.61/11.26 40.61/11.26 (3) DependencyGraphProof (EQUIVALENT) 40.61/11.26 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. 40.61/11.26 ---------------------------------------- 40.61/11.26 40.61/11.26 (4) 40.61/11.26 Obligation: 40.61/11.26 Q DP problem: 40.61/11.26 The TRS P consists of the following rules: 40.61/11.26 40.61/11.26 A(c(x1)) -> A(x1) 40.61/11.26 A(c(x1)) -> A(a(x1)) 40.61/11.26 40.61/11.26 The TRS R consists of the following rules: 40.61/11.26 40.61/11.26 a(b(x1)) -> x1 40.61/11.26 a(c(x1)) -> c(b(b(c(a(a(x1)))))) 40.61/11.26 b(c(x1)) -> x1 40.61/11.26 40.61/11.26 Q is empty. 40.61/11.26 We have to consider all minimal (P,Q,R)-chains. 40.61/11.26 ---------------------------------------- 40.61/11.26 40.61/11.26 (5) QDPOrderProof (EQUIVALENT) 40.61/11.26 We use the reduction pair processor [LPAR04,JAR06]. 40.61/11.26 40.61/11.26 40.61/11.26 The following pairs can be oriented strictly and are deleted. 40.61/11.26 40.61/11.26 A(c(x1)) -> A(x1) 40.61/11.26 The remaining pairs can at least be oriented weakly. 40.61/11.26 Used ordering: Polynomial Order [NEGPOLO,POLO] with Interpretation: 40.61/11.26 40.61/11.26 POL( A_1(x_1) ) = 2x_1 40.61/11.26 POL( a_1(x_1) ) = x_1 + 2 40.61/11.26 POL( b_1(x_1) ) = max{0, x_1 - 2} 40.61/11.26 POL( c_1(x_1) ) = x_1 + 2 40.61/11.26 40.61/11.26 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 40.61/11.26 40.61/11.26 a(b(x1)) -> x1 40.61/11.26 a(c(x1)) -> c(b(b(c(a(a(x1)))))) popout

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