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SRS_Relative 2019-03-29 08.12 pair #432296313
details
property
value
status
complete
benchmark
random-95.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n004.star.cs.uiowa.edu
space
Waldmann_19
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
2.24782 seconds
cpu usage
5.73384
user time
5.4769
system time
0.256936
max virtual memory
1.9283676E7
max residence set size
528188.0
stage attributes
key
value
starexec-result
YES
output
5.47/2.17 YES 5.47/2.19 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 5.47/2.19 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 5.47/2.19 5.47/2.19 5.47/2.19 Termination of the given RelTRS could be proven: 5.47/2.19 5.47/2.19 (0) RelTRS 5.47/2.19 (1) RelTRS S Cleaner [EQUIVALENT, 0 ms] 5.47/2.19 (2) RelTRS 5.47/2.19 (3) RelTRSRRRProof [EQUIVALENT, 38 ms] 5.47/2.19 (4) RelTRS 5.47/2.19 (5) RIsEmptyProof [EQUIVALENT, 1 ms] 5.47/2.19 (6) YES 5.47/2.19 5.47/2.19 5.47/2.19 ---------------------------------------- 5.47/2.19 5.47/2.19 (0) 5.47/2.19 Obligation: 5.47/2.19 Relative term rewrite system: 5.47/2.19 The relative TRS consists of the following R rules: 5.47/2.19 5.47/2.19 a(b(c(x1))) -> c(c(c(x1))) 5.47/2.19 b(a(b(x1))) -> c(a(a(x1))) 5.47/2.19 5.47/2.19 The relative TRS consists of the following S rules: 5.47/2.19 5.47/2.19 b(c(a(x1))) -> a(a(c(x1))) 5.47/2.19 a(c(c(x1))) -> c(b(a(x1))) 5.47/2.19 b(a(b(x1))) -> b(c(c(x1))) 5.47/2.19 b(b(c(x1))) -> a(c(b(x1))) 5.47/2.19 c(a(a(x1))) -> c(a(a(x1))) 5.47/2.19 5.47/2.19 5.47/2.19 ---------------------------------------- 5.47/2.19 5.47/2.19 (1) RelTRS S Cleaner (EQUIVALENT) 5.47/2.19 We have deleted all rules from S that have the shape t -> t: 5.47/2.19 5.47/2.19 c(a(a(x1))) -> c(a(a(x1))) 5.47/2.19 5.47/2.19 5.47/2.19 ---------------------------------------- 5.47/2.19 5.47/2.19 (2) 5.47/2.19 Obligation: 5.47/2.19 Relative term rewrite system: 5.47/2.19 The relative TRS consists of the following R rules: 5.47/2.19 5.47/2.19 a(b(c(x1))) -> c(c(c(x1))) 5.47/2.19 b(a(b(x1))) -> c(a(a(x1))) 5.47/2.19 5.47/2.19 The relative TRS consists of the following S rules: 5.47/2.19 5.47/2.19 b(c(a(x1))) -> a(a(c(x1))) 5.47/2.19 a(c(c(x1))) -> c(b(a(x1))) 5.47/2.19 b(a(b(x1))) -> b(c(c(x1))) 5.47/2.19 b(b(c(x1))) -> a(c(b(x1))) 5.47/2.19 5.47/2.19 5.47/2.19 ---------------------------------------- 5.47/2.19 5.47/2.19 (3) RelTRSRRRProof (EQUIVALENT) 5.47/2.19 We used the following monotonic ordering for rule removal: 5.47/2.19 Knuth-Bendix order [KBO] with precedence:b_1 > a_1 > c_1 5.47/2.19 5.47/2.19 and weight map: 5.47/2.19 5.47/2.19 a_1=1 5.47/2.19 b_1=1 5.47/2.19 c_1=1 5.47/2.19 5.47/2.19 The variable weight is 1With this ordering the following rules can be removed [MATRO] because they are oriented strictly: 5.47/2.19 Rules from R: 5.47/2.19 5.47/2.19 a(b(c(x1))) -> c(c(c(x1))) 5.47/2.19 b(a(b(x1))) -> c(a(a(x1))) 5.47/2.19 Rules from S: 5.47/2.19 5.47/2.19 b(c(a(x1))) -> a(a(c(x1))) 5.47/2.19 a(c(c(x1))) -> c(b(a(x1))) 5.47/2.19 b(a(b(x1))) -> b(c(c(x1))) 5.47/2.19 b(b(c(x1))) -> a(c(b(x1))) 5.47/2.19 5.47/2.19 5.47/2.19 5.47/2.19 5.47/2.19 ---------------------------------------- 5.47/2.19 5.47/2.19 (4) 5.47/2.19 Obligation: 5.47/2.19 Relative term rewrite system: 5.47/2.19 R is empty. 5.47/2.19 S is empty. 5.47/2.19 5.47/2.19 ---------------------------------------- 5.47/2.19 5.47/2.19 (5) RIsEmptyProof (EQUIVALENT) 5.47/2.19 The TRS R is empty. Hence, termination is trivially proven.
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