details

property	value
status	complete
benchmark	size-12-alpha-3-num-553.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n091.star.cs.uiowa.edu
space	Waldmann_07_size12

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	11.9959 seconds
cpu usage	43.1357
user time	41.5333
system time	1.60238
max virtual memory	4.2007216E7
max residence set size	4286800.0

stage attributes

key	value
starexec-result	YES

output

42.53/11.82 YES 42.85/11.90 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 42.85/11.90 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 42.85/11.90 42.85/11.90 42.85/11.90 Termination w.r.t. Q of the given QTRS could be proven: 42.85/11.90 42.85/11.90 (0) QTRS 42.85/11.90 (1) DependencyPairsProof [EQUIVALENT, 9 ms] 42.85/11.90 (2) QDP 42.85/11.90 (3) DependencyGraphProof [EQUIVALENT, 0 ms] 42.85/11.90 (4) QDP 42.85/11.90 (5) QDPOrderProof [EQUIVALENT, 40 ms] 42.85/11.90 (6) QDP 42.85/11.90 (7) QDPOrderProof [EQUIVALENT, 41 ms] 42.85/11.90 (8) QDP 42.85/11.90 (9) PisEmptyProof [EQUIVALENT, 0 ms] 42.85/11.90 (10) YES 42.85/11.90 42.85/11.90 42.85/11.90 ---------------------------------------- 42.85/11.90 42.85/11.90 (0) 42.85/11.90 Obligation: 42.85/11.90 Q restricted rewrite system: 42.85/11.90 The TRS R consists of the following rules: 42.85/11.90 42.85/11.90 a(b(x1)) -> x1 42.85/11.90 a(c(x1)) -> b(c(c(b(a(a(x1)))))) 42.85/11.90 b(c(x1)) -> x1 42.85/11.90 42.85/11.90 Q is empty. 42.85/11.90 42.85/11.90 ---------------------------------------- 42.85/11.90 42.85/11.90 (1) DependencyPairsProof (EQUIVALENT) 42.85/11.90 Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. 42.85/11.90 ---------------------------------------- 42.85/11.90 42.85/11.90 (2) 42.85/11.90 Obligation: 42.85/11.90 Q DP problem: 42.85/11.90 The TRS P consists of the following rules: 42.85/11.90 42.85/11.90 A(c(x1)) -> B(c(c(b(a(a(x1)))))) 42.85/11.90 A(c(x1)) -> B(a(a(x1))) 42.85/11.90 A(c(x1)) -> A(a(x1)) 42.85/11.90 A(c(x1)) -> A(x1) 42.85/11.90 42.85/11.90 The TRS R consists of the following rules: 42.85/11.90 42.85/11.90 a(b(x1)) -> x1 42.85/11.90 a(c(x1)) -> b(c(c(b(a(a(x1)))))) 42.85/11.90 b(c(x1)) -> x1 42.85/11.90 42.85/11.90 Q is empty. 42.85/11.90 We have to consider all minimal (P,Q,R)-chains. 42.85/11.90 ---------------------------------------- 42.85/11.90 42.85/11.90 (3) DependencyGraphProof (EQUIVALENT) 42.85/11.90 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. 42.85/11.90 ---------------------------------------- 42.85/11.90 42.85/11.90 (4) 42.85/11.90 Obligation: 42.85/11.90 Q DP problem: 42.85/11.90 The TRS P consists of the following rules: 42.85/11.90 42.85/11.90 A(c(x1)) -> A(x1) 42.85/11.90 A(c(x1)) -> A(a(x1)) 42.85/11.90 42.85/11.90 The TRS R consists of the following rules: 42.85/11.90 42.85/11.90 a(b(x1)) -> x1 42.85/11.90 a(c(x1)) -> b(c(c(b(a(a(x1)))))) 42.85/11.90 b(c(x1)) -> x1 42.85/11.90 42.85/11.90 Q is empty. 42.85/11.90 We have to consider all minimal (P,Q,R)-chains. 42.85/11.90 ---------------------------------------- 42.85/11.90 42.85/11.90 (5) QDPOrderProof (EQUIVALENT) 42.85/11.90 We use the reduction pair processor [LPAR04,JAR06]. 42.85/11.90 42.85/11.90 42.85/11.90 The following pairs can be oriented strictly and are deleted. 42.85/11.90 42.85/11.90 A(c(x1)) -> A(x1) 42.85/11.90 The remaining pairs can at least be oriented weakly. 42.85/11.90 Used ordering: Polynomial Order [NEGPOLO,POLO] with Interpretation: 42.85/11.90 42.85/11.90 POL( A_1(x_1) ) = max{0, x_1 - 1} 42.85/11.90 POL( a_1(x_1) ) = x_1 + 2 42.85/11.90 POL( b_1(x_1) ) = max{0, x_1 - 2} 42.85/11.90 POL( c_1(x_1) ) = x_1 + 2 42.85/11.90 42.85/11.90 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 42.85/11.90 42.85/11.90 a(b(x1)) -> x1 42.85/11.90 a(c(x1)) -> b(c(c(b(a(a(x1)))))) popout

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all output return to SRS_Standard 2019-03-29 03.29