details

property	value
status	complete
benchmark	size-12-alpha-3-num-354.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n052.star.cs.uiowa.edu
space	Waldmann_07_size12

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	8.90081 seconds
cpu usage	31.3881
user time	30.2059
system time	1.18221
max virtual memory	4.1976436E7
max residence set size	3375756.0

stage attributes

key	value
starexec-result	YES

output

30.56/8.67 YES 30.91/8.81 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 30.91/8.81 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 30.91/8.81 30.91/8.81 30.91/8.81 Termination w.r.t. Q of the given QTRS could be proven: 30.91/8.81 30.91/8.81 (0) QTRS 30.91/8.81 (1) DependencyPairsProof [EQUIVALENT, 0 ms] 30.91/8.81 (2) QDP 30.91/8.81 (3) DependencyGraphProof [EQUIVALENT, 0 ms] 30.91/8.81 (4) QDP 30.91/8.81 (5) MRRProof [EQUIVALENT, 10 ms] 30.91/8.81 (6) QDP 30.91/8.81 (7) QDPOrderProof [EQUIVALENT, 864 ms] 30.91/8.81 (8) QDP 30.91/8.81 (9) PisEmptyProof [EQUIVALENT, 0 ms] 30.91/8.81 (10) YES 30.91/8.81 30.91/8.81 30.91/8.81 ---------------------------------------- 30.91/8.81 30.91/8.81 (0) 30.91/8.81 Obligation: 30.91/8.81 Q restricted rewrite system: 30.91/8.81 The TRS R consists of the following rules: 30.91/8.81 30.91/8.81 a(x1) -> b(x1) 30.91/8.81 a(b(x1)) -> c(a(c(a(x1)))) 30.91/8.81 c(b(c(x1))) -> b(x1) 30.91/8.81 30.91/8.81 Q is empty. 30.91/8.81 30.91/8.81 ---------------------------------------- 30.91/8.81 30.91/8.81 (1) DependencyPairsProof (EQUIVALENT) 30.91/8.81 Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. 30.91/8.81 ---------------------------------------- 30.91/8.81 30.91/8.81 (2) 30.91/8.81 Obligation: 30.91/8.81 Q DP problem: 30.91/8.81 The TRS P consists of the following rules: 30.91/8.81 30.91/8.81 A(b(x1)) -> C(a(c(a(x1)))) 30.91/8.81 A(b(x1)) -> A(c(a(x1))) 30.91/8.81 A(b(x1)) -> C(a(x1)) 30.91/8.81 A(b(x1)) -> A(x1) 30.91/8.81 30.91/8.81 The TRS R consists of the following rules: 30.91/8.81 30.91/8.81 a(x1) -> b(x1) 30.91/8.81 a(b(x1)) -> c(a(c(a(x1)))) 30.91/8.81 c(b(c(x1))) -> b(x1) 30.91/8.81 30.91/8.81 Q is empty. 30.91/8.81 We have to consider all minimal (P,Q,R)-chains. 30.91/8.81 ---------------------------------------- 30.91/8.81 30.91/8.81 (3) DependencyGraphProof (EQUIVALENT) 30.91/8.81 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. 30.91/8.81 ---------------------------------------- 30.91/8.81 30.91/8.81 (4) 30.91/8.81 Obligation: 30.91/8.81 Q DP problem: 30.91/8.81 The TRS P consists of the following rules: 30.91/8.81 30.91/8.81 A(b(x1)) -> A(x1) 30.91/8.81 A(b(x1)) -> A(c(a(x1))) 30.91/8.81 30.91/8.81 The TRS R consists of the following rules: 30.91/8.81 30.91/8.81 a(x1) -> b(x1) 30.91/8.81 a(b(x1)) -> c(a(c(a(x1)))) 30.91/8.81 c(b(c(x1))) -> b(x1) 30.91/8.81 30.91/8.81 Q is empty. 30.91/8.81 We have to consider all minimal (P,Q,R)-chains. 30.91/8.81 ---------------------------------------- 30.91/8.81 30.91/8.81 (5) MRRProof (EQUIVALENT) 30.91/8.81 By using the rule removal processor [LPAR04] with the following ordering, at least one Dependency Pair or term rewrite system rule of this QDP problem can be strictly oriented. 30.91/8.81 30.91/8.81 Strictly oriented dependency pairs: 30.91/8.81 30.91/8.81 A(b(x1)) -> A(x1) 30.91/8.81 30.91/8.81 30.91/8.81 Used ordering: Polynomial interpretation [POLO]: 30.91/8.81 30.91/8.81 POL(A(x_1)) = 2*x_1 30.91/8.81 POL(a(x_1)) = 2 + x_1 30.91/8.81 POL(b(x_1)) = 2 + x_1 30.91/8.81 POL(c(x_1)) = x_1 30.91/8.81 30.91/8.81 30.91/8.81 ---------------------------------------- 30.91/8.81 30.91/8.81 (6) popout

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