details

property	value
status	complete
benchmark	size-12-alpha-3-num-552.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n156.star.cs.uiowa.edu
space	Waldmann_07_size12

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	9.53503 seconds
cpu usage	33.7113
user time	32.1327
system time	1.57857
max virtual memory	2.0470632E7
max residence set size	4137112.0

stage attributes

key	value
starexec-result	YES

output

33.15/9.40 YES 33.57/9.47 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 33.57/9.47 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 33.57/9.47 33.57/9.47 33.57/9.47 Termination w.r.t. Q of the given QTRS could be proven: 33.57/9.47 33.57/9.47 (0) QTRS 33.57/9.47 (1) DependencyPairsProof [EQUIVALENT, 23 ms] 33.57/9.47 (2) QDP 33.57/9.47 (3) DependencyGraphProof [EQUIVALENT, 0 ms] 33.57/9.47 (4) QDP 33.57/9.47 (5) QDPOrderProof [EQUIVALENT, 73 ms] 33.57/9.47 (6) QDP 33.57/9.47 (7) PisEmptyProof [EQUIVALENT, 0 ms] 33.57/9.47 (8) YES 33.57/9.47 33.57/9.47 33.57/9.47 ---------------------------------------- 33.57/9.47 33.57/9.47 (0) 33.57/9.47 Obligation: 33.57/9.47 Q restricted rewrite system: 33.57/9.47 The TRS R consists of the following rules: 33.57/9.47 33.57/9.47 a(b(x1)) -> x1 33.57/9.47 a(c(x1)) -> b(c(c(a(a(b(x1)))))) 33.57/9.47 b(c(x1)) -> x1 33.57/9.47 33.57/9.47 Q is empty. 33.57/9.47 33.57/9.47 ---------------------------------------- 33.57/9.47 33.57/9.47 (1) DependencyPairsProof (EQUIVALENT) 33.57/9.47 Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. 33.57/9.47 ---------------------------------------- 33.57/9.47 33.57/9.47 (2) 33.57/9.47 Obligation: 33.57/9.47 Q DP problem: 33.57/9.47 The TRS P consists of the following rules: 33.57/9.47 33.57/9.47 A(c(x1)) -> B(c(c(a(a(b(x1)))))) 33.57/9.47 A(c(x1)) -> A(a(b(x1))) 33.57/9.47 A(c(x1)) -> A(b(x1)) 33.57/9.47 A(c(x1)) -> B(x1) 33.57/9.47 33.57/9.47 The TRS R consists of the following rules: 33.57/9.47 33.57/9.47 a(b(x1)) -> x1 33.57/9.47 a(c(x1)) -> b(c(c(a(a(b(x1)))))) 33.57/9.47 b(c(x1)) -> x1 33.57/9.47 33.57/9.47 Q is empty. 33.57/9.47 We have to consider all minimal (P,Q,R)-chains. 33.57/9.47 ---------------------------------------- 33.57/9.47 33.57/9.47 (3) DependencyGraphProof (EQUIVALENT) 33.57/9.47 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. 33.57/9.47 ---------------------------------------- 33.57/9.47 33.57/9.47 (4) 33.57/9.47 Obligation: 33.57/9.47 Q DP problem: 33.57/9.47 The TRS P consists of the following rules: 33.57/9.47 33.57/9.47 A(c(x1)) -> A(b(x1)) 33.57/9.47 A(c(x1)) -> A(a(b(x1))) 33.57/9.47 33.57/9.47 The TRS R consists of the following rules: 33.57/9.47 33.57/9.47 a(b(x1)) -> x1 33.57/9.47 a(c(x1)) -> b(c(c(a(a(b(x1)))))) 33.57/9.47 b(c(x1)) -> x1 33.57/9.47 33.57/9.47 Q is empty. 33.57/9.47 We have to consider all minimal (P,Q,R)-chains. 33.57/9.47 ---------------------------------------- 33.57/9.47 33.57/9.47 (5) QDPOrderProof (EQUIVALENT) 33.57/9.47 We use the reduction pair processor [LPAR04,JAR06]. 33.57/9.47 33.57/9.47 33.57/9.47 The following pairs can be oriented strictly and are deleted. 33.57/9.47 33.57/9.47 A(c(x1)) -> A(b(x1)) 33.57/9.47 A(c(x1)) -> A(a(b(x1))) 33.57/9.47 The remaining pairs can at least be oriented weakly. 33.57/9.47 Used ordering: Polynomial interpretation [POLO,RATPOLO]: 33.57/9.47 33.57/9.47 POL(A(x_1)) = [1/2]x_1 33.57/9.47 POL(a(x_1)) = [4]x_1 33.57/9.47 POL(b(x_1)) = [1/4]x_1 33.57/9.47 POL(c(x_1)) = [1/2] + [4]x_1 33.57/9.47 The value of delta used in the strict ordering is 1/4. 33.57/9.47 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 33.57/9.47 33.57/9.47 b(c(x1)) -> x1 33.57/9.47 a(b(x1)) -> x1 33.57/9.47 a(c(x1)) -> b(c(c(a(a(b(x1)))))) popout

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all output return to SRS_Standard 2019-03-29 03.29