details

property	value
status	complete
benchmark	size-12-alpha-3-num-40.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n180.star.cs.uiowa.edu
space	Waldmann_07_size12

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	9.92521 seconds
cpu usage	68.8777
user time	65.8552
system time	3.02256
max virtual memory	2.1013104E7
max residence set size	4156320.0

stage attributes

key	value
starexec-result	YES

output

34.21/9.84 YES 34.21/9.85 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 34.21/9.85 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 34.21/9.85 34.21/9.85 34.21/9.85 Termination w.r.t. Q of the given QTRS could be proven: 34.21/9.85 34.21/9.85 (0) QTRS 34.21/9.85 (1) DependencyPairsProof [EQUIVALENT, 17 ms] 34.21/9.85 (2) QDP 34.21/9.85 (3) QDPOrderProof [EQUIVALENT, 133 ms] 34.21/9.85 (4) QDP 34.21/9.85 (5) DependencyGraphProof [EQUIVALENT, 0 ms] 34.21/9.85 (6) QDP 34.21/9.85 (7) QDPOrderProof [EQUIVALENT, 13 ms] 34.21/9.85 (8) QDP 34.21/9.85 (9) QDPOrderProof [EQUIVALENT, 0 ms] 34.21/9.85 (10) QDP 34.21/9.85 (11) PisEmptyProof [EQUIVALENT, 0 ms] 34.21/9.85 (12) YES 34.21/9.85 34.21/9.85 34.21/9.85 ---------------------------------------- 34.21/9.85 34.21/9.85 (0) 34.21/9.85 Obligation: 34.21/9.85 Q restricted rewrite system: 34.21/9.85 The TRS R consists of the following rules: 34.21/9.85 34.21/9.85 a(x1) -> x1 34.21/9.85 a(x1) -> b(b(c(x1))) 34.21/9.85 c(c(a(x1))) -> a(a(c(c(x1)))) 34.21/9.85 34.21/9.85 Q is empty. 34.21/9.85 34.21/9.85 ---------------------------------------- 34.21/9.85 34.21/9.85 (1) DependencyPairsProof (EQUIVALENT) 34.21/9.85 Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. 34.21/9.85 ---------------------------------------- 34.21/9.85 34.21/9.85 (2) 34.21/9.85 Obligation: 34.21/9.85 Q DP problem: 34.21/9.85 The TRS P consists of the following rules: 34.21/9.85 34.21/9.85 A(x1) -> C(x1) 34.21/9.85 C(c(a(x1))) -> A(a(c(c(x1)))) 34.21/9.85 C(c(a(x1))) -> A(c(c(x1))) 34.21/9.85 C(c(a(x1))) -> C(c(x1)) 34.21/9.85 C(c(a(x1))) -> C(x1) 34.21/9.85 34.21/9.85 The TRS R consists of the following rules: 34.21/9.85 34.21/9.85 a(x1) -> x1 34.21/9.85 a(x1) -> b(b(c(x1))) 34.21/9.85 c(c(a(x1))) -> a(a(c(c(x1)))) 34.21/9.85 34.21/9.85 Q is empty. 34.21/9.85 We have to consider all minimal (P,Q,R)-chains. 34.21/9.85 ---------------------------------------- 34.21/9.85 34.21/9.85 (3) QDPOrderProof (EQUIVALENT) 34.21/9.85 We use the reduction pair processor [LPAR04,JAR06]. 34.21/9.85 34.21/9.85 34.21/9.85 The following pairs can be oriented strictly and are deleted. 34.21/9.85 34.21/9.85 A(x1) -> C(x1) 34.21/9.85 The remaining pairs can at least be oriented weakly. 34.21/9.85 Used ordering: Matrix interpretation [MATRO] with arctic natural numbers [ARCTIC]: 34.21/9.85 34.21/9.85 <<< 34.21/9.85 POL(A(x_1)) = [[1A]] + [[0A, 1A, 1A]] * x_1 34.21/9.85 >>> 34.21/9.85 34.21/9.85 <<< 34.21/9.85 POL(C(x_1)) = [[0A]] + [[-I, 0A, 0A]] * x_1 34.21/9.85 >>> 34.21/9.85 34.21/9.85 <<< 34.21/9.85 POL(c(x_1)) = [[0A], [0A], [0A]] + [[-I, 0A, -I], [1A, -I, 0A], [0A, -I, -I]] * x_1 34.21/9.85 >>> 34.21/9.85 34.21/9.85 <<< 34.21/9.85 POL(a(x_1)) = [[1A], [-I], [0A]] + [[0A, 1A, -I], [-I, 0A, -I], [-I, -I, 0A]] * x_1 34.21/9.85 >>> 34.21/9.85 34.21/9.85 <<< 34.21/9.85 POL(b(x_1)) = [[0A], [-I], [-I]] + [[-I, -I, -I], [-I, -I, -I], [0A, 0A, -I]] * x_1 34.21/9.85 >>> 34.21/9.85 34.21/9.85 34.21/9.85 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 34.21/9.85 34.21/9.85 c(c(a(x1))) -> a(a(c(c(x1)))) 34.21/9.85 a(x1) -> x1 34.21/9.85 a(x1) -> b(b(c(x1))) 34.21/9.85 34.21/9.85 popout

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