details

property	value
status	complete
benchmark	random-227.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n167.star.cs.uiowa.edu
space	Waldmann_19

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	4.51643 seconds
cpu usage	29.067
user time	27.7351
system time	1.33194
max virtual memory	3.8042776E7
max residence set size	1452836.0

stage attributes

key	value
starexec-result	YES

output

14.14/4.35 YES 14.34/4.41 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 14.34/4.41 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 14.34/4.41 14.34/4.41 14.34/4.41 Termination of the given RelTRS could be proven: 14.34/4.41 14.34/4.41 (0) RelTRS 14.34/4.41 (1) RelTRSRRRProof [EQUIVALENT, 425 ms] 14.34/4.41 (2) RelTRS 14.34/4.41 (3) SIsEmptyProof [EQUIVALENT, 0 ms] 14.34/4.41 (4) QTRS 14.34/4.41 (5) RFCMatchBoundsTRSProof [EQUIVALENT, 7 ms] 14.34/4.41 (6) YES 14.34/4.41 14.34/4.41 14.34/4.41 ---------------------------------------- 14.34/4.41 14.34/4.41 (0) 14.34/4.41 Obligation: 14.34/4.41 Relative term rewrite system: 14.34/4.41 The relative TRS consists of the following R rules: 14.34/4.41 14.34/4.41 c(b(c(x1))) -> c(a(b(x1))) 14.34/4.41 c(b(b(x1))) -> a(a(c(x1))) 14.34/4.41 a(a(b(x1))) -> b(b(c(x1))) 14.34/4.41 b(b(c(x1))) -> a(b(c(x1))) 14.34/4.41 b(b(b(x1))) -> b(a(b(x1))) 14.34/4.41 14.34/4.41 The relative TRS consists of the following S rules: 14.34/4.41 14.34/4.41 c(b(a(x1))) -> b(a(c(x1))) 14.34/4.41 14.34/4.41 14.34/4.41 ---------------------------------------- 14.34/4.41 14.34/4.41 (1) RelTRSRRRProof (EQUIVALENT) 14.34/4.41 We used the following monotonic ordering for rule removal: 14.34/4.41 Matrix interpretation [MATRO] to (N^2, +, *, >=, >) : 14.34/4.41 14.34/4.41 <<< 14.34/4.41 POL(c(x_1)) = [[0], [2]] + [[2, 0], [0, 2]] * x_1 14.34/4.41 >>> 14.34/4.41 14.34/4.41 <<< 14.34/4.41 POL(b(x_1)) = [[2], [0]] + [[2, 2], [0, 0]] * x_1 14.34/4.41 >>> 14.34/4.41 14.34/4.41 <<< 14.34/4.41 POL(a(x_1)) = [[2], [0]] + [[2, 0], [0, 0]] * x_1 14.34/4.41 >>> 14.34/4.41 14.34/4.41 With this ordering the following rules can be removed [MATRO] because they are oriented strictly: 14.34/4.41 Rules from R: 14.34/4.41 14.34/4.41 c(b(b(x1))) -> a(a(c(x1))) 14.34/4.41 Rules from S: 14.34/4.41 14.34/4.41 c(b(a(x1))) -> b(a(c(x1))) 14.34/4.41 14.34/4.41 14.34/4.41 14.34/4.41 14.34/4.41 ---------------------------------------- 14.34/4.41 14.34/4.41 (2) 14.34/4.41 Obligation: 14.34/4.41 Relative term rewrite system: 14.34/4.41 The relative TRS consists of the following R rules: 14.34/4.41 14.34/4.41 c(b(c(x1))) -> c(a(b(x1))) 14.34/4.41 a(a(b(x1))) -> b(b(c(x1))) 14.34/4.41 b(b(c(x1))) -> a(b(c(x1))) 14.34/4.41 b(b(b(x1))) -> b(a(b(x1))) 14.34/4.41 14.34/4.41 S is empty. 14.34/4.41 14.34/4.41 ---------------------------------------- 14.34/4.41 14.34/4.41 (3) SIsEmptyProof (EQUIVALENT) 14.34/4.41 The TRS S is empty. Hence, termination of R/S is equivalent to termination of R. 14.34/4.41 ---------------------------------------- 14.34/4.41 14.34/4.41 (4) 14.34/4.41 Obligation: 14.34/4.41 Q restricted rewrite system: 14.34/4.41 The TRS R consists of the following rules: 14.34/4.41 14.34/4.41 c(b(c(x1))) -> c(a(b(x1))) 14.34/4.41 a(a(b(x1))) -> b(b(c(x1))) 14.34/4.41 b(b(c(x1))) -> a(b(c(x1))) 14.34/4.41 b(b(b(x1))) -> b(a(b(x1))) 14.34/4.41 14.34/4.41 Q is empty. 14.34/4.41 14.34/4.41 ---------------------------------------- 14.34/4.41 14.34/4.41 (5) RFCMatchBoundsTRSProof (EQUIVALENT) 14.34/4.41 Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 3. This implies Q-termination of R. 14.34/4.41 The following rules were used to construct the certificate: popout

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all output return to SRS_Relative 2019-03-29 08.12