details

property	value
status	complete
benchmark	r9.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n103.star.cs.uiowa.edu
space	Waldmann_06_relative

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	7.62171 seconds
cpu usage	26.6279
user time	25.7951
system time	0.832782
max virtual memory	5.8227476E7
max residence set size	1695192.0

stage attributes

key	value
starexec-result	YES

output

26.37/7.54 YES 26.37/7.55 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 26.37/7.55 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 26.37/7.55 26.37/7.55 26.37/7.55 Termination of the given RelTRS could be proven: 26.37/7.55 26.37/7.55 (0) RelTRS 26.37/7.55 (1) RelTRSRRRProof [EQUIVALENT, 1398 ms] 26.37/7.55 (2) RelTRS 26.37/7.55 (3) SIsEmptyProof [EQUIVALENT, 0 ms] 26.37/7.55 (4) QTRS 26.37/7.55 (5) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms] 26.37/7.55 (6) YES 26.37/7.55 26.37/7.55 26.37/7.55 ---------------------------------------- 26.37/7.55 26.37/7.55 (0) 26.37/7.55 Obligation: 26.37/7.55 Relative term rewrite system: 26.37/7.55 The relative TRS consists of the following R rules: 26.37/7.55 26.37/7.55 b(a(b(x1))) -> b(a(a(a(b(x1))))) 26.37/7.55 26.37/7.55 The relative TRS consists of the following S rules: 26.37/7.55 26.37/7.55 a(a(a(x1))) -> b(b(b(b(x1)))) 26.37/7.55 26.37/7.55 26.37/7.55 ---------------------------------------- 26.37/7.55 26.37/7.55 (1) RelTRSRRRProof (EQUIVALENT) 26.37/7.55 We used the following monotonic ordering for rule removal: 26.37/7.55 Matrix interpretation [MATRO] to (N^6, +, *, >=, >) : 26.37/7.55 26.37/7.55 <<< 26.37/7.55 POL(b(x_1)) = [[0], [0], [0], [1], [0], [0]] + [[1, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0]] * x_1 26.37/7.55 >>> 26.37/7.55 26.37/7.55 <<< 26.37/7.55 POL(a(x_1)) = [[0], [0], [0], [0], [1], [0]] + [[1, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 1, 0, 0, 1], [0, 0, 0, 1, 0, 0]] * x_1 26.37/7.55 >>> 26.37/7.55 26.37/7.55 With this ordering the following rules can be removed [MATRO] because they are oriented strictly: 26.37/7.55 Rules from R: 26.37/7.55 none 26.37/7.55 Rules from S: 26.37/7.55 26.37/7.55 a(a(a(x1))) -> b(b(b(b(x1)))) 26.37/7.55 26.37/7.55 26.37/7.55 26.37/7.55 26.37/7.55 ---------------------------------------- 26.37/7.55 26.37/7.55 (2) 26.37/7.55 Obligation: 26.37/7.55 Relative term rewrite system: 26.37/7.55 The relative TRS consists of the following R rules: 26.37/7.55 26.37/7.55 b(a(b(x1))) -> b(a(a(a(b(x1))))) 26.37/7.55 26.37/7.55 S is empty. 26.37/7.55 26.37/7.55 ---------------------------------------- 26.37/7.55 26.37/7.55 (3) SIsEmptyProof (EQUIVALENT) 26.37/7.55 The TRS S is empty. Hence, termination of R/S is equivalent to termination of R. 26.37/7.55 ---------------------------------------- 26.37/7.55 26.37/7.55 (4) 26.37/7.55 Obligation: 26.37/7.55 Q restricted rewrite system: 26.37/7.55 The TRS R consists of the following rules: 26.37/7.55 26.37/7.55 b(a(b(x1))) -> b(a(a(a(b(x1))))) 26.37/7.55 26.37/7.55 Q is empty. 26.37/7.55 26.37/7.55 ---------------------------------------- 26.37/7.55 26.37/7.55 (5) RFCMatchBoundsTRSProof (EQUIVALENT) 26.37/7.55 Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 1. This implies Q-termination of R. 26.37/7.55 The following rules were used to construct the certificate: 26.37/7.55 26.37/7.55 b(a(b(x1))) -> b(a(a(a(b(x1))))) 26.37/7.55 26.37/7.55 The certificate found is represented by the following graph. 26.37/7.55 The certificate consists of the following enumerated nodes: 26.37/7.55 133, 134, 135, 136, 137, 138, 139, 140, 141, 142 26.37/7.55 26.37/7.55 Node 133 is start node and node 134 is final node. 26.37/7.55 26.37/7.55 Those nodes are connected through the following edges: 26.37/7.55 26.37/7.55 * 133 to 135 labelled b_1(0)* 134 to 134 labelled #_1(0)* 135 to 136 labelled a_1(0)* 136 to 137 labelled a_1(0)* 137 to 138 labelled a_1(0)* 138 to 134 labelled b_1(0)* 138 to 139 labelled b_1(1)* 139 to 140 labelled a_1(1)* 140 to 141 labelled a_1(1)* 141 to 142 labelled a_1(1)* 142 to 134 labelled b_1(1)* 142 to 139 labelled b_1(1) 26.37/7.55 26.37/7.55 26.37/7.55 ---------------------------------------- popout

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all output return to SRS_Relative 2019-03-29 08.12