details

property	value
status	complete
benchmark	random-66.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n129.star.cs.uiowa.edu
space	Waldmann_19

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	4.44108 seconds
cpu usage	14.0375
user time	13.3653
system time	0.672192
max virtual memory	2.101964E7
max residence set size	1818684.0

stage attributes

key	value
starexec-result	YES

output

13.44/4.25 YES 13.70/4.33 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 13.70/4.33 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 13.70/4.33 13.70/4.33 13.70/4.33 Termination of the given RelTRS could be proven: 13.70/4.33 13.70/4.33 (0) RelTRS 13.70/4.33 (1) RelTRSRRRProof [EQUIVALENT, 56 ms] 13.70/4.33 (2) RelTRS 13.70/4.33 (3) SIsEmptyProof [EQUIVALENT, 0 ms] 13.70/4.33 (4) QTRS 13.70/4.33 (5) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms] 13.70/4.33 (6) YES 13.70/4.33 13.70/4.33 13.70/4.33 ---------------------------------------- 13.70/4.33 13.70/4.33 (0) 13.70/4.33 Obligation: 13.70/4.33 Relative term rewrite system: 13.70/4.33 The relative TRS consists of the following R rules: 13.70/4.33 13.70/4.33 c(a(b(x1))) -> a(b(c(x1))) 13.70/4.33 a(b(a(x1))) -> c(a(a(x1))) 13.70/4.33 c(c(c(x1))) -> b(c(c(x1))) 13.70/4.33 b(b(a(x1))) -> b(b(b(x1))) 13.70/4.33 13.70/4.33 The relative TRS consists of the following S rules: 13.70/4.33 13.70/4.33 a(c(b(x1))) -> c(b(c(x1))) 13.70/4.33 a(c(b(x1))) -> b(b(c(x1))) 13.70/4.33 13.70/4.33 13.70/4.33 ---------------------------------------- 13.70/4.33 13.70/4.33 (1) RelTRSRRRProof (EQUIVALENT) 13.70/4.33 We used the following monotonic ordering for rule removal: 13.70/4.33 Polynomial interpretation [POLO]: 13.70/4.33 13.70/4.33 POL(a(x_1)) = 1 + x_1 13.70/4.33 POL(b(x_1)) = x_1 13.70/4.33 POL(c(x_1)) = x_1 13.70/4.33 With this ordering the following rules can be removed [MATRO] because they are oriented strictly: 13.70/4.33 Rules from R: 13.70/4.33 13.70/4.33 b(b(a(x1))) -> b(b(b(x1))) 13.70/4.33 Rules from S: 13.70/4.33 13.70/4.33 a(c(b(x1))) -> c(b(c(x1))) 13.70/4.33 a(c(b(x1))) -> b(b(c(x1))) 13.70/4.33 13.70/4.33 13.70/4.33 13.70/4.33 13.70/4.33 ---------------------------------------- 13.70/4.33 13.70/4.33 (2) 13.70/4.33 Obligation: 13.70/4.33 Relative term rewrite system: 13.70/4.33 The relative TRS consists of the following R rules: 13.70/4.33 13.70/4.33 c(a(b(x1))) -> a(b(c(x1))) 13.70/4.33 a(b(a(x1))) -> c(a(a(x1))) 13.70/4.33 c(c(c(x1))) -> b(c(c(x1))) 13.70/4.33 13.70/4.33 S is empty. 13.70/4.33 13.70/4.33 ---------------------------------------- 13.70/4.33 13.70/4.33 (3) SIsEmptyProof (EQUIVALENT) 13.70/4.33 The TRS S is empty. Hence, termination of R/S is equivalent to termination of R. 13.70/4.33 ---------------------------------------- 13.70/4.33 13.70/4.33 (4) 13.70/4.33 Obligation: 13.70/4.33 Q restricted rewrite system: 13.70/4.33 The TRS R consists of the following rules: 13.70/4.33 13.70/4.33 c(a(b(x1))) -> a(b(c(x1))) 13.70/4.33 a(b(a(x1))) -> c(a(a(x1))) 13.70/4.33 c(c(c(x1))) -> b(c(c(x1))) 13.70/4.33 13.70/4.33 Q is empty. 13.70/4.33 13.70/4.33 ---------------------------------------- 13.70/4.33 13.70/4.33 (5) RFCMatchBoundsTRSProof (EQUIVALENT) 13.70/4.33 Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 3. This implies Q-termination of R. 13.70/4.33 The following rules were used to construct the certificate: 13.70/4.33 13.70/4.33 c(a(b(x1))) -> a(b(c(x1))) 13.70/4.33 a(b(a(x1))) -> c(a(a(x1))) 13.70/4.33 c(c(c(x1))) -> b(c(c(x1))) 13.70/4.33 13.70/4.33 The certificate found is represented by the following graph. 13.70/4.33 The certificate consists of the following enumerated nodes: 13.70/4.33 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 165, 166, 167, 168, 169, 170, 171, 172 13.70/4.33 13.70/4.33 Node 129 is start node and node 130 is final node. popout

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all output return to SRS_Relative 2019-03-29 08.12