details

property	value
status	complete
benchmark	02.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n086.star.cs.uiowa.edu
space	Mixed_SRS

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	10.2848 seconds
cpu usage	31.5
user time	30.1495
system time	1.35048
max virtual memory	1.03899536E8
max residence set size	3870260.0

stage attributes

key	value
starexec-result	YES

output

29.30/8.41 YES 31.29/9.13 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 31.29/9.13 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 31.29/9.13 31.29/9.13 31.29/9.13 Termination w.r.t. Q of the given QTRS could be proven: 31.29/9.13 31.29/9.13 (0) QTRS 31.29/9.13 (1) DependencyPairsProof [EQUIVALENT, 22 ms] 31.29/9.13 (2) QDP 31.29/9.13 (3) QDPOrderProof [EQUIVALENT, 38 ms] 31.29/9.13 (4) QDP 31.29/9.13 (5) QDPOrderProof [EQUIVALENT, 0 ms] 31.29/9.13 (6) QDP 31.29/9.13 (7) DependencyGraphProof [EQUIVALENT, 0 ms] 31.29/9.13 (8) TRUE 31.29/9.13 31.29/9.13 31.29/9.13 ---------------------------------------- 31.29/9.13 31.29/9.13 (0) 31.29/9.13 Obligation: 31.29/9.13 Q restricted rewrite system: 31.29/9.13 The TRS R consists of the following rules: 31.29/9.13 31.29/9.13 a(a(a(a(x1)))) -> b(a(a(b(x1)))) 31.29/9.13 b(a(b(x1))) -> a(b(a(x1))) 31.29/9.13 31.29/9.13 Q is empty. 31.29/9.13 31.29/9.13 ---------------------------------------- 31.29/9.13 31.29/9.13 (1) DependencyPairsProof (EQUIVALENT) 31.29/9.13 Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. 31.29/9.13 ---------------------------------------- 31.29/9.13 31.29/9.13 (2) 31.29/9.13 Obligation: 31.29/9.13 Q DP problem: 31.29/9.13 The TRS P consists of the following rules: 31.29/9.13 31.29/9.13 A(a(a(a(x1)))) -> B(a(a(b(x1)))) 31.29/9.13 A(a(a(a(x1)))) -> A(a(b(x1))) 31.29/9.13 A(a(a(a(x1)))) -> A(b(x1)) 31.29/9.13 A(a(a(a(x1)))) -> B(x1) 31.29/9.13 B(a(b(x1))) -> A(b(a(x1))) 31.29/9.13 B(a(b(x1))) -> B(a(x1)) 31.29/9.13 B(a(b(x1))) -> A(x1) 31.29/9.13 31.29/9.13 The TRS R consists of the following rules: 31.29/9.13 31.29/9.13 a(a(a(a(x1)))) -> b(a(a(b(x1)))) 31.29/9.13 b(a(b(x1))) -> a(b(a(x1))) 31.29/9.13 31.29/9.13 Q is empty. 31.29/9.13 We have to consider all minimal (P,Q,R)-chains. 31.29/9.13 ---------------------------------------- 31.29/9.13 31.29/9.13 (3) QDPOrderProof (EQUIVALENT) 31.29/9.13 We use the reduction pair processor [LPAR04,JAR06]. 31.29/9.13 31.29/9.13 31.29/9.13 The following pairs can be oriented strictly and are deleted. 31.29/9.13 31.29/9.13 A(a(a(a(x1)))) -> A(a(b(x1))) 31.29/9.13 A(a(a(a(x1)))) -> A(b(x1)) 31.29/9.13 A(a(a(a(x1)))) -> B(x1) 31.29/9.13 B(a(b(x1))) -> B(a(x1)) 31.29/9.13 B(a(b(x1))) -> A(x1) 31.29/9.13 The remaining pairs can at least be oriented weakly. 31.29/9.13 Used ordering: Polynomial interpretation [POLO]: 31.29/9.13 31.29/9.13 POL(A(x_1)) = 1 + x_1 31.29/9.13 POL(B(x_1)) = 1 + x_1 31.29/9.13 POL(a(x_1)) = 1 + x_1 31.29/9.13 POL(b(x_1)) = 1 + x_1 31.29/9.13 31.29/9.13 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 31.29/9.13 31.29/9.13 b(a(b(x1))) -> a(b(a(x1))) 31.29/9.13 a(a(a(a(x1)))) -> b(a(a(b(x1)))) 31.29/9.13 31.29/9.13 31.29/9.13 ---------------------------------------- 31.29/9.13 31.29/9.13 (4) 31.29/9.13 Obligation: 31.29/9.13 Q DP problem: 31.29/9.13 The TRS P consists of the following rules: 31.29/9.13 31.29/9.13 A(a(a(a(x1)))) -> B(a(a(b(x1)))) 31.29/9.13 B(a(b(x1))) -> A(b(a(x1))) 31.29/9.13 31.29/9.13 The TRS R consists of the following rules: 31.29/9.13 31.29/9.13 a(a(a(a(x1)))) -> b(a(a(b(x1)))) 31.29/9.13 b(a(b(x1))) -> a(b(a(x1))) 31.29/9.13 31.29/9.13 Q is empty. 31.29/9.13 We have to consider all minimal (P,Q,R)-chains. popout

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