details

property	value
status	complete
benchmark	hom02.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n053.star.cs.uiowa.edu
space	Trafo_06

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	3.2005 seconds
cpu usage	9.20648
user time	8.72327
system time	0.483211
max virtual memory	3.9769952E7
max residence set size	1062296.0

stage attributes

key	value
starexec-result	YES

output

8.77/3.06 YES 8.77/3.09 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 8.77/3.09 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 8.77/3.09 8.77/3.09 8.77/3.09 Termination w.r.t. Q of the given QTRS could be proven: 8.77/3.09 8.77/3.09 (0) QTRS 8.77/3.09 (1) QTRSRRRProof [EQUIVALENT, 69 ms] 8.77/3.09 (2) QTRS 8.77/3.09 (3) DependencyPairsProof [EQUIVALENT, 0 ms] 8.77/3.09 (4) QDP 8.77/3.09 (5) DependencyGraphProof [EQUIVALENT, 0 ms] 8.77/3.09 (6) QDP 8.77/3.09 (7) MRRProof [EQUIVALENT, 63 ms] 8.77/3.09 (8) QDP 8.77/3.09 (9) PisEmptyProof [EQUIVALENT, 0 ms] 8.77/3.09 (10) YES 8.77/3.09 8.77/3.09 8.77/3.09 ---------------------------------------- 8.77/3.09 8.77/3.09 (0) 8.77/3.09 Obligation: 8.77/3.09 Q restricted rewrite system: 8.77/3.09 The TRS R consists of the following rules: 8.77/3.09 8.77/3.09 a(x1) -> b(b(x1)) 8.77/3.09 a(b(b(x1))) -> b(b(c(c(c(a(x1)))))) 8.77/3.09 b(b(x1)) -> c(c(c(x1))) 8.77/3.09 c(c(c(b(b(x1))))) -> a(x1) 8.77/3.09 8.77/3.09 Q is empty. 8.77/3.09 8.77/3.09 ---------------------------------------- 8.77/3.09 8.77/3.09 (1) QTRSRRRProof (EQUIVALENT) 8.77/3.09 Used ordering: 8.77/3.09 Polynomial interpretation [POLO]: 8.77/3.09 8.77/3.09 POL(a(x_1)) = 2 + x_1 8.77/3.09 POL(b(x_1)) = 1 + x_1 8.77/3.09 POL(c(x_1)) = x_1 8.77/3.09 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: 8.77/3.09 8.77/3.09 b(b(x1)) -> c(c(c(x1))) 8.77/3.09 8.77/3.09 8.77/3.09 8.77/3.09 8.77/3.09 ---------------------------------------- 8.77/3.09 8.77/3.09 (2) 8.77/3.09 Obligation: 8.77/3.09 Q restricted rewrite system: 8.77/3.09 The TRS R consists of the following rules: 8.77/3.09 8.77/3.09 a(x1) -> b(b(x1)) 8.77/3.09 a(b(b(x1))) -> b(b(c(c(c(a(x1)))))) 8.77/3.09 c(c(c(b(b(x1))))) -> a(x1) 8.77/3.09 8.77/3.09 Q is empty. 8.77/3.09 8.77/3.09 ---------------------------------------- 8.77/3.09 8.77/3.09 (3) DependencyPairsProof (EQUIVALENT) 8.77/3.09 Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. 8.77/3.09 ---------------------------------------- 8.77/3.09 8.77/3.09 (4) 8.77/3.09 Obligation: 8.77/3.09 Q DP problem: 8.77/3.09 The TRS P consists of the following rules: 8.77/3.09 8.77/3.09 A(b(b(x1))) -> C(c(c(a(x1)))) 8.77/3.09 A(b(b(x1))) -> C(c(a(x1))) 8.77/3.09 A(b(b(x1))) -> C(a(x1)) 8.77/3.09 A(b(b(x1))) -> A(x1) 8.77/3.09 C(c(c(b(b(x1))))) -> A(x1) 8.77/3.09 8.77/3.09 The TRS R consists of the following rules: 8.77/3.09 8.77/3.09 a(x1) -> b(b(x1)) 8.77/3.09 a(b(b(x1))) -> b(b(c(c(c(a(x1)))))) 8.77/3.09 c(c(c(b(b(x1))))) -> a(x1) 8.77/3.09 8.77/3.09 Q is empty. 8.77/3.09 We have to consider all minimal (P,Q,R)-chains. 8.77/3.09 ---------------------------------------- 8.77/3.09 8.77/3.09 (5) DependencyGraphProof (EQUIVALENT) 8.77/3.09 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. 8.77/3.09 ---------------------------------------- 8.77/3.09 8.77/3.09 (6) 8.77/3.09 Obligation: 8.77/3.09 Q DP problem: 8.77/3.09 The TRS P consists of the following rules: 8.77/3.09 8.77/3.09 C(c(c(b(b(x1))))) -> A(x1) popout

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all output return to SRS_Standard 2019-03-29 03.29