details

property	value
status	complete
benchmark	size-12-alpha-2-num-22.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n166.star.cs.uiowa.edu
space	Waldmann_07_size12

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	4.92073 seconds
cpu usage	15.9288
user time	15.2617
system time	0.667117
max virtual memory	1.9886116E7
max residence set size	1969808.0

stage attributes

key	value
starexec-result	YES

output

15.10/4.69 YES 15.61/4.86 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 15.61/4.86 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 15.61/4.86 15.61/4.86 15.61/4.86 Termination w.r.t. Q of the given QTRS could be proven: 15.61/4.86 15.61/4.86 (0) QTRS 15.61/4.86 (1) DependencyPairsProof [EQUIVALENT, 1 ms] 15.61/4.86 (2) QDP 15.61/4.86 (3) QDPOrderProof [EQUIVALENT, 180 ms] 15.61/4.86 (4) QDP 15.61/4.86 (5) DependencyGraphProof [EQUIVALENT, 0 ms] 15.61/4.86 (6) TRUE 15.61/4.86 15.61/4.86 15.61/4.86 ---------------------------------------- 15.61/4.86 15.61/4.86 (0) 15.61/4.86 Obligation: 15.61/4.86 Q restricted rewrite system: 15.61/4.86 The TRS R consists of the following rules: 15.61/4.86 15.61/4.86 a(x1) -> x1 15.61/4.86 a(a(b(a(x1)))) -> b(b(a(a(a(x1))))) 15.61/4.86 b(x1) -> a(x1) 15.61/4.86 15.61/4.86 Q is empty. 15.61/4.86 15.61/4.86 ---------------------------------------- 15.61/4.86 15.61/4.86 (1) DependencyPairsProof (EQUIVALENT) 15.61/4.86 Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. 15.61/4.86 ---------------------------------------- 15.61/4.86 15.61/4.86 (2) 15.61/4.86 Obligation: 15.61/4.86 Q DP problem: 15.61/4.86 The TRS P consists of the following rules: 15.61/4.86 15.61/4.86 A(a(b(a(x1)))) -> B(b(a(a(a(x1))))) 15.61/4.86 A(a(b(a(x1)))) -> B(a(a(a(x1)))) 15.61/4.86 A(a(b(a(x1)))) -> A(a(a(x1))) 15.61/4.86 A(a(b(a(x1)))) -> A(a(x1)) 15.61/4.86 B(x1) -> A(x1) 15.61/4.86 15.61/4.86 The TRS R consists of the following rules: 15.61/4.86 15.61/4.86 a(x1) -> x1 15.61/4.86 a(a(b(a(x1)))) -> b(b(a(a(a(x1))))) 15.61/4.86 b(x1) -> a(x1) 15.61/4.86 15.61/4.86 Q is empty. 15.61/4.86 We have to consider all minimal (P,Q,R)-chains. 15.61/4.86 ---------------------------------------- 15.61/4.86 15.61/4.86 (3) QDPOrderProof (EQUIVALENT) 15.61/4.86 We use the reduction pair processor [LPAR04,JAR06]. 15.61/4.86 15.61/4.86 15.61/4.86 The following pairs can be oriented strictly and are deleted. 15.61/4.86 15.61/4.86 A(a(b(a(x1)))) -> B(b(a(a(a(x1))))) 15.61/4.86 A(a(b(a(x1)))) -> B(a(a(a(x1)))) 15.61/4.86 A(a(b(a(x1)))) -> A(a(a(x1))) 15.61/4.86 A(a(b(a(x1)))) -> A(a(x1)) 15.61/4.86 The remaining pairs can at least be oriented weakly. 15.61/4.86 Used ordering: Matrix interpretation [MATRO] with arctic natural numbers [ARCTIC]: 15.61/4.86 15.61/4.86 <<< 15.61/4.86 POL(A(x_1)) = [[0A]] + [[-I, -I, 0A]] * x_1 15.61/4.86 >>> 15.61/4.86 15.61/4.86 <<< 15.61/4.86 POL(a(x_1)) = [[-I], [0A], [-I]] + [[0A, -I, 0A], [0A, 0A, 0A], [0A, -I, 0A]] * x_1 15.61/4.86 >>> 15.61/4.86 15.61/4.86 <<< 15.61/4.86 POL(b(x_1)) = [[1A], [0A], [-I]] + [[0A, 0A, 1A], [0A, 0A, 0A], [0A, -I, 0A]] * x_1 15.61/4.86 >>> 15.61/4.86 15.61/4.86 <<< 15.61/4.86 POL(B(x_1)) = [[0A]] + [[-I, -I, 0A]] * x_1 15.61/4.86 >>> 15.61/4.86 15.61/4.86 15.61/4.86 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 15.61/4.86 15.61/4.86 a(x1) -> x1 15.61/4.86 a(a(b(a(x1)))) -> b(b(a(a(a(x1))))) 15.61/4.86 b(x1) -> a(x1) 15.61/4.86 15.61/4.86 15.61/4.86 ---------------------------------------- 15.61/4.86 15.61/4.86 (4) 15.61/4.86 Obligation: 15.61/4.86 Q DP problem: 15.61/4.86 The TRS P consists of the following rules: 15.61/4.86 popout

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