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SRS_Standard 2019-03-29 03.29 pair #432289459
details
property
value
status
complete
benchmark
size-12-alpha-3-num-279.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n138.star.cs.uiowa.edu
space
Waldmann_07_size12
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
8.93362 seconds
cpu usage
31.3015
user time
29.9454
system time
1.35611
max virtual memory
8.3699112E7
max residence set size
3836832.0
stage attributes
key
value
starexec-result
YES
output
30.50/8.78 YES 31.05/8.81 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 31.05/8.81 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 31.05/8.81 31.05/8.81 31.05/8.81 Termination w.r.t. Q of the given QTRS could be proven: 31.05/8.81 31.05/8.81 (0) QTRS 31.05/8.81 (1) DependencyPairsProof [EQUIVALENT, 0 ms] 31.05/8.81 (2) QDP 31.05/8.81 (3) QDPOrderProof [EQUIVALENT, 156 ms] 31.05/8.81 (4) QDP 31.05/8.81 (5) DependencyGraphProof [EQUIVALENT, 0 ms] 31.05/8.81 (6) QDP 31.05/8.81 (7) UsableRulesProof [EQUIVALENT, 0 ms] 31.05/8.81 (8) QDP 31.05/8.81 (9) QDPSizeChangeProof [EQUIVALENT, 0 ms] 31.05/8.81 (10) YES 31.05/8.81 31.05/8.81 31.05/8.81 ---------------------------------------- 31.05/8.81 31.05/8.81 (0) 31.05/8.81 Obligation: 31.05/8.81 Q restricted rewrite system: 31.05/8.81 The TRS R consists of the following rules: 31.05/8.81 31.05/8.81 a(x1) -> x1 31.05/8.81 a(b(x1)) -> c(b(x1)) 31.05/8.81 b(x1) -> a(a(c(x1))) 31.05/8.81 c(c(x1)) -> b(x1) 31.05/8.81 31.05/8.81 Q is empty. 31.05/8.81 31.05/8.81 ---------------------------------------- 31.05/8.81 31.05/8.81 (1) DependencyPairsProof (EQUIVALENT) 31.05/8.81 Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. 31.05/8.81 ---------------------------------------- 31.05/8.81 31.05/8.81 (2) 31.05/8.81 Obligation: 31.05/8.81 Q DP problem: 31.05/8.81 The TRS P consists of the following rules: 31.05/8.81 31.05/8.81 A(b(x1)) -> C(b(x1)) 31.05/8.81 B(x1) -> A(a(c(x1))) 31.05/8.81 B(x1) -> A(c(x1)) 31.05/8.81 B(x1) -> C(x1) 31.05/8.81 C(c(x1)) -> B(x1) 31.05/8.81 31.05/8.81 The TRS R consists of the following rules: 31.05/8.81 31.05/8.81 a(x1) -> x1 31.05/8.81 a(b(x1)) -> c(b(x1)) 31.05/8.81 b(x1) -> a(a(c(x1))) 31.05/8.81 c(c(x1)) -> b(x1) 31.05/8.81 31.05/8.81 Q is empty. 31.05/8.81 We have to consider all minimal (P,Q,R)-chains. 31.05/8.81 ---------------------------------------- 31.05/8.81 31.05/8.81 (3) QDPOrderProof (EQUIVALENT) 31.05/8.81 We use the reduction pair processor [LPAR04,JAR06]. 31.05/8.81 31.05/8.81 31.05/8.81 The following pairs can be oriented strictly and are deleted. 31.05/8.81 31.05/8.81 A(b(x1)) -> C(b(x1)) 31.05/8.81 The remaining pairs can at least be oriented weakly. 31.05/8.81 Used ordering: Matrix interpretation [MATRO] with arctic natural numbers [ARCTIC]: 31.05/8.81 31.05/8.81 <<< 31.05/8.81 POL(A(x_1)) = [[-I]] + [[0A, 0A, -I]] * x_1 31.05/8.81 >>> 31.05/8.81 31.05/8.81 <<< 31.05/8.81 POL(b(x_1)) = [[-I], [0A], [0A]] + [[0A, 0A, 0A], [1A, 1A, 1A], [1A, 1A, 1A]] * x_1 31.05/8.81 >>> 31.05/8.81 31.05/8.81 <<< 31.05/8.81 POL(C(x_1)) = [[-I]] + [[0A, -I, -I]] * x_1 31.05/8.81 >>> 31.05/8.81 31.05/8.81 <<< 31.05/8.81 POL(B(x_1)) = [[-I]] + [[0A, 0A, 0A]] * x_1 31.05/8.81 >>> 31.05/8.81 31.05/8.81 <<< 31.05/8.81 POL(a(x_1)) = [[-I], [-I], [0A]] + [[0A, 0A, -I], [0A, 0A, -I], [0A, 1A, 0A]] * x_1 31.05/8.81 >>> 31.05/8.81 31.05/8.81 <<< 31.05/8.81 POL(c(x_1)) = [[-I], [-I], [0A]] + [[0A, 0A, 0A], [0A, 0A, 0A], [1A, 1A, 1A]] * x_1 31.05/8.81 >>> 31.05/8.81 31.05/8.81 31.05/8.81 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 31.05/8.81 31.05/8.81 a(b(x1)) -> c(b(x1))
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