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SRS_Standard 2019-03-29 03.29 pair #432293971
details
property
value
status
complete
benchmark
3.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n102.star.cs.uiowa.edu
space
Secret_06_SRS
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
98.4 seconds
cpu usage
384.436
user time
378.372
system time
6.06454
max virtual memory
8.0495824E7
max residence set size
7284168.0
stage attributes
key
value
starexec-result
YES
output
383.92/98.28 YES 384.31/98.34 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 384.31/98.34 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 384.31/98.34 384.31/98.34 384.31/98.34 Termination w.r.t. Q of the given QTRS could be proven: 384.31/98.34 384.31/98.34 (0) QTRS 384.31/98.34 (1) DependencyPairsProof [EQUIVALENT, 0 ms] 384.31/98.34 (2) QDP 384.31/98.34 (3) QDPOrderProof [EQUIVALENT, 469 ms] 384.31/98.34 (4) QDP 384.31/98.34 (5) QDPOrderProof [EQUIVALENT, 51 ms] 384.31/98.34 (6) QDP 384.31/98.34 (7) QDPOrderProof [EQUIVALENT, 223 ms] 384.31/98.34 (8) QDP 384.31/98.34 (9) QDPOrderProof [EQUIVALENT, 2868 ms] 384.31/98.34 (10) QDP 384.31/98.34 (11) QDPOrderProof [EQUIVALENT, 1517 ms] 384.31/98.34 (12) QDP 384.31/98.34 (13) DependencyGraphProof [EQUIVALENT, 0 ms] 384.31/98.34 (14) QDP 384.31/98.34 (15) UsableRulesProof [EQUIVALENT, 0 ms] 384.31/98.34 (16) QDP 384.31/98.34 (17) QDPSizeChangeProof [EQUIVALENT, 0 ms] 384.31/98.34 (18) YES 384.31/98.34 384.31/98.34 384.31/98.34 ---------------------------------------- 384.31/98.34 384.31/98.34 (0) 384.31/98.34 Obligation: 384.31/98.34 Q restricted rewrite system: 384.31/98.34 The TRS R consists of the following rules: 384.31/98.34 384.31/98.34 a(a(a(b(x1)))) -> b(a(b(a(x1)))) 384.31/98.34 b(b(a(x1))) -> a(a(a(b(x1)))) 384.31/98.34 384.31/98.34 Q is empty. 384.31/98.34 384.31/98.34 ---------------------------------------- 384.31/98.34 384.31/98.34 (1) DependencyPairsProof (EQUIVALENT) 384.31/98.34 Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. 384.31/98.34 ---------------------------------------- 384.31/98.34 384.31/98.34 (2) 384.31/98.34 Obligation: 384.31/98.34 Q DP problem: 384.31/98.34 The TRS P consists of the following rules: 384.31/98.34 384.31/98.34 A(a(a(b(x1)))) -> B(a(b(a(x1)))) 384.31/98.34 A(a(a(b(x1)))) -> A(b(a(x1))) 384.31/98.34 A(a(a(b(x1)))) -> B(a(x1)) 384.31/98.34 A(a(a(b(x1)))) -> A(x1) 384.31/98.34 B(b(a(x1))) -> A(a(a(b(x1)))) 384.31/98.34 B(b(a(x1))) -> A(a(b(x1))) 384.31/98.34 B(b(a(x1))) -> A(b(x1)) 384.31/98.34 B(b(a(x1))) -> B(x1) 384.31/98.34 384.31/98.34 The TRS R consists of the following rules: 384.31/98.34 384.31/98.34 a(a(a(b(x1)))) -> b(a(b(a(x1)))) 384.31/98.34 b(b(a(x1))) -> a(a(a(b(x1)))) 384.31/98.34 384.31/98.34 Q is empty. 384.31/98.34 We have to consider all minimal (P,Q,R)-chains. 384.31/98.34 ---------------------------------------- 384.31/98.34 384.31/98.34 (3) QDPOrderProof (EQUIVALENT) 384.31/98.34 We use the reduction pair processor [LPAR04,JAR06]. 384.31/98.34 384.31/98.34 384.31/98.34 The following pairs can be oriented strictly and are deleted. 384.31/98.34 384.31/98.34 A(a(a(b(x1)))) -> B(a(b(a(x1)))) 384.31/98.34 The remaining pairs can at least be oriented weakly. 384.31/98.34 Used ordering: Matrix interpretation [MATRO] with arctic natural numbers [ARCTIC]: 384.31/98.34 384.31/98.34 <<< 384.31/98.34 POL(A(x_1)) = [[0A]] + [[0A, 0A, 0A]] * x_1 384.31/98.34 >>> 384.31/98.34 384.31/98.34 <<< 384.31/98.34 POL(a(x_1)) = [[0A], [0A], [0A]] + [[-I, 0A, -I], [-I, -I, 0A], [0A, -I, -I]] * x_1 384.31/98.34 >>> 384.31/98.34 384.31/98.34 <<< 384.31/98.34 POL(b(x_1)) = [[0A], [1A], [1A]] + [[-I, -I, -I], [0A, 0A, 0A], [0A, 0A, 0A]] * x_1 384.31/98.34 >>> 384.31/98.34 384.31/98.34 <<< 384.31/98.34 POL(B(x_1)) = [[0A]] + [[-I, -I, 0A]] * x_1 384.31/98.34 >>> 384.31/98.34 384.31/98.34 384.31/98.34 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 384.31/98.34 384.31/98.34 b(b(a(x1))) -> a(a(a(b(x1)))) 384.31/98.34 a(a(a(b(x1)))) -> b(a(b(a(x1))))
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