details

property	value
status	complete
benchmark	sym-2.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n141.star.cs.uiowa.edu
space	Waldmann_06_SRS

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	11.1464 seconds
cpu usage	39.5263
user time	37.6439
system time	1.88246
max virtual memory	6.2852084E7
max residence set size	4389344.0

stage attributes

key	value
starexec-result	YES

output

37.90/10.73 YES 39.13/11.05 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 39.13/11.05 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 39.13/11.05 39.13/11.05 39.13/11.05 Termination w.r.t. Q of the given QTRS could be proven: 39.13/11.05 39.13/11.05 (0) QTRS 39.13/11.05 (1) DependencyPairsProof [EQUIVALENT, 20 ms] 39.13/11.05 (2) QDP 39.13/11.05 (3) QDPOrderProof [EQUIVALENT, 151 ms] 39.13/11.05 (4) QDP 39.13/11.05 (5) QDPOrderProof [EQUIVALENT, 0 ms] 39.13/11.05 (6) QDP 39.13/11.05 (7) QDPOrderProof [EQUIVALENT, 39 ms] 39.13/11.05 (8) QDP 39.13/11.05 (9) DependencyGraphProof [EQUIVALENT, 0 ms] 39.13/11.05 (10) QDP 39.13/11.05 (11) QDPOrderProof [EQUIVALENT, 92 ms] 39.13/11.05 (12) QDP 39.13/11.05 (13) PisEmptyProof [EQUIVALENT, 0 ms] 39.13/11.05 (14) YES 39.13/11.05 39.13/11.05 39.13/11.05 ---------------------------------------- 39.13/11.05 39.13/11.05 (0) 39.13/11.05 Obligation: 39.13/11.05 Q restricted rewrite system: 39.13/11.05 The TRS R consists of the following rules: 39.13/11.05 39.13/11.05 a(a(a(x1))) -> b(b(b(x1))) 39.13/11.05 b(a(a(b(x1)))) -> x1 39.13/11.05 b(a(a(b(x1)))) -> b(a(a(a(b(x1))))) 39.13/11.05 39.13/11.05 Q is empty. 39.13/11.05 39.13/11.05 ---------------------------------------- 39.13/11.05 39.13/11.05 (1) DependencyPairsProof (EQUIVALENT) 39.13/11.05 Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. 39.13/11.05 ---------------------------------------- 39.13/11.05 39.13/11.05 (2) 39.13/11.05 Obligation: 39.13/11.05 Q DP problem: 39.13/11.05 The TRS P consists of the following rules: 39.13/11.05 39.13/11.05 A(a(a(x1))) -> B(b(b(x1))) 39.13/11.05 A(a(a(x1))) -> B(b(x1)) 39.13/11.05 A(a(a(x1))) -> B(x1) 39.13/11.05 B(a(a(b(x1)))) -> B(a(a(a(b(x1))))) 39.13/11.05 B(a(a(b(x1)))) -> A(a(a(b(x1)))) 39.13/11.05 39.13/11.05 The TRS R consists of the following rules: 39.13/11.05 39.13/11.05 a(a(a(x1))) -> b(b(b(x1))) 39.13/11.05 b(a(a(b(x1)))) -> x1 39.13/11.05 b(a(a(b(x1)))) -> b(a(a(a(b(x1))))) 39.13/11.05 39.13/11.05 Q is empty. 39.13/11.05 We have to consider all minimal (P,Q,R)-chains. 39.13/11.05 ---------------------------------------- 39.13/11.05 39.13/11.05 (3) QDPOrderProof (EQUIVALENT) 39.13/11.05 We use the reduction pair processor [LPAR04,JAR06]. 39.13/11.05 39.13/11.05 39.13/11.05 The following pairs can be oriented strictly and are deleted. 39.13/11.05 39.13/11.05 A(a(a(x1))) -> B(x1) 39.13/11.05 The remaining pairs can at least be oriented weakly. 39.13/11.05 Used ordering: Matrix interpretation [MATRO] with arctic natural numbers [ARCTIC]: 39.13/11.05 39.13/11.05 <<< 39.13/11.05 POL(A(x_1)) = [[1A]] + [[-I, -I, 1A]] * x_1 39.13/11.05 >>> 39.13/11.05 39.13/11.05 <<< 39.13/11.05 POL(a(x_1)) = [[-I], [0A], [0A]] + [[0A, 0A, 0A], [1A, 0A, 0A], [0A, -I, -I]] * x_1 39.13/11.05 >>> 39.13/11.05 39.13/11.05 <<< 39.13/11.05 POL(B(x_1)) = [[0A]] + [[0A, 0A, 0A]] * x_1 39.13/11.05 >>> 39.13/11.05 39.13/11.05 <<< 39.13/11.05 POL(b(x_1)) = [[0A], [1A], [-I]] + [[-I, -I, 0A], [0A, 0A, 1A], [-I, -I, 0A]] * x_1 39.13/11.05 >>> 39.13/11.05 39.13/11.05 39.13/11.05 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 39.13/11.05 39.13/11.05 b(a(a(b(x1)))) -> x1 39.13/11.05 b(a(a(b(x1)))) -> b(a(a(a(b(x1))))) 39.13/11.05 a(a(a(x1))) -> b(b(b(x1))) 39.13/11.05 39.13/11.05 39.13/11.05 ---------------------------------------- 39.13/11.05 popout

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