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SRS_Relative 2019-03-29 08.12 pair #432296408
details
property
value
status
complete
benchmark
random-137.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n170.star.cs.uiowa.edu
space
Waldmann_19
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.87656 seconds
cpu usage
3.83586
user time
3.65854
system time
0.177319
max virtual memory
1.9074756E7
max residence set size
274476.0
stage attributes
key
value
starexec-result
YES
output
3.69/1.82 YES 3.69/1.84 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 3.69/1.84 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 3.69/1.84 3.69/1.84 3.69/1.84 Termination w.r.t. Q of the given QTRS could be proven: 3.69/1.84 3.69/1.84 (0) QTRS 3.69/1.84 (1) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms] 3.69/1.84 (2) YES 3.69/1.84 3.69/1.84 3.69/1.84 ---------------------------------------- 3.69/1.84 3.69/1.84 (0) 3.69/1.84 Obligation: 3.69/1.84 Q restricted rewrite system: 3.69/1.84 The TRS R consists of the following rules: 3.69/1.84 3.69/1.84 a(c(a(x1))) -> b(a(c(x1))) 3.69/1.84 a(c(c(x1))) -> a(b(b(x1))) 3.69/1.84 c(a(a(x1))) -> a(a(a(x1))) 3.69/1.84 b(c(c(x1))) -> a(c(a(x1))) 3.69/1.84 b(a(a(x1))) -> b(c(b(x1))) 3.69/1.84 3.69/1.84 Q is empty. 3.69/1.84 3.69/1.84 ---------------------------------------- 3.69/1.84 3.69/1.84 (1) RFCMatchBoundsTRSProof (EQUIVALENT) 3.69/1.84 Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 3. This implies Q-termination of R. 3.69/1.84 The following rules were used to construct the certificate: 3.69/1.84 3.69/1.84 a(c(a(x1))) -> b(a(c(x1))) 3.69/1.84 a(c(c(x1))) -> a(b(b(x1))) 3.69/1.84 c(a(a(x1))) -> a(a(a(x1))) 3.69/1.84 b(c(c(x1))) -> a(c(a(x1))) 3.69/1.84 b(a(a(x1))) -> b(c(b(x1))) 3.69/1.84 3.69/1.84 The certificate found is represented by the following graph. 3.69/1.84 The certificate consists of the following enumerated nodes: 3.69/1.84 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 49, 50, 51, 52, 53, 54, 55, 56, 69, 70 3.69/1.84 3.69/1.84 Node 1 is start node and node 2 is final node. 3.69/1.84 3.69/1.84 Those nodes are connected through the following edges: 3.69/1.84 3.69/1.84 * 1 to 3 labelled b_1(0)* 1 to 5 labelled a_1(0)* 1 to 7 labelled a_1(0)* 1 to 9 labelled a_1(0)* 1 to 11 labelled b_1(0)* 1 to 19 labelled b_1(1)* 1 to 23 labelled b_1(1)* 1 to 49 labelled b_1(2)* 1 to 55 labelled b_1(2)* 2 to 2 labelled #_1(0)* 3 to 4 labelled a_1(0)* 3 to 19 labelled b_1(1)* 3 to 21 labelled a_1(1)* 3 to 49 labelled b_1(2)* 4 to 2 labelled c_1(0)* 4 to 13 labelled a_1(1)* 5 to 6 labelled b_1(0)* 5 to 23 labelled b_1(1)* 5 to 55 labelled b_1(2)* 6 to 2 labelled b_1(0)* 6 to 15 labelled a_1(1)* 6 to 17 labelled b_1(1)* 6 to 25 labelled b_1(2)* 6 to 55 labelled b_1(2)* 6 to 49 labelled b_1(2)* 7 to 8 labelled a_1(0)* 8 to 2 labelled a_1(0)* 8 to 19 labelled b_1(1)* 8 to 21 labelled a_1(1)* 8 to 49 labelled b_1(2)* 9 to 10 labelled c_1(0)* 9 to 13 labelled a_1(1)* 10 to 2 labelled a_1(0)* 10 to 19 labelled b_1(1)* 10 to 21 labelled a_1(1)* 10 to 49 labelled b_1(2)* 11 to 12 labelled c_1(0)* 11 to 19 labelled a_1(1)* 12 to 2 labelled b_1(0)* 12 to 15 labelled a_1(1)* 12 to 17 labelled b_1(1)* 12 to 25 labelled b_1(2)* 12 to 55 labelled b_1(2)* 12 to 49 labelled b_1(2)* 13 to 14 labelled a_1(1)* 14 to 2 labelled a_1(1)* 14 to 19 labelled b_1(1)* 14 to 21 labelled a_1(1)* 14 to 49 labelled b_1(2)* 15 to 16 labelled c_1(1)* 15 to 13 labelled a_1(1)* 16 to 2 labelled a_1(1)* 16 to 19 labelled b_1(1)* 16 to 21 labelled a_1(1)* 16 to 49 labelled b_1(2)* 17 to 18 labelled c_1(1)* 17 to 51 labelled a_1(2)* 18 to 2 labelled b_1(1)* 18 to 15 labelled a_1(1)* 18 to 17 labelled b_1(1)* 18 to 25 labelled b_1(2)* 18 to 55 labelled b_1(2)* 18 to 49 labelled b_1(2)* 19 to 20 labelled a_1(1)* 19 to 19 labelled b_1(1)* 19 to 21 labelled a_1(1)* 19 to 49 labelled b_1(2)* 20 to 2 labelled c_1(1)* 20 to 13 labelled a_1(1)* 20 to 21 labelled c_1(1)* 21 to 22 labelled b_1(1)* 21 to 49 labelled b_1(2)* 22 to 2 labelled b_1(1)* 22 to 15 labelled a_1(1)* 22 to 17 labelled b_1(1)* 22 to 25 labelled b_1(2)* 22 to 55 labelled b_1(2)* 22 to 49 labelled b_1(2)* 23 to 24 labelled c_1(1)* 23 to 51 labelled a_1(2)* 24 to 13 labelled b_1(1)* 24 to 53 labelled b_1(2)* 24 to 20 labelled b_1(1)* 24 to 21 labelled b_1(1)* 24 to 15 labelled a_1(1)* 24 to 25 labelled b_1(2)* 24 to 69 labelled b_1(3)* 24 to 49 labelled b_1(2)* 25 to 26 labelled a_1(2)* 25 to 19 labelled b_1(1)* 25 to 21 labelled a_1(1)* 25 to 49 labelled b_1(2)* 26 to 2 labelled c_1(2)* 26 to 13 labelled a_1(1)* 26 to 21 labelled c_1(2)* 49 to 50 labelled c_1(2)* 50 to 13 labelled b_1(2)* 50 to 53 labelled b_1(2)* 50 to 69 labelled b_1(3)* 51 to 52 labelled a_1(2)* 52 to 13 labelled a_1(2)* 53 to 54 labelled c_1(2)* 53 to 51 labelled a_1(2)* 54 to 2 labelled b_1(2)* 54 to 21 labelled b_1(2)* 54 to 15 labelled a_1(1)* 54 to 17 labelled b_1(1)* 54 to 25 labelled b_1(2)* 54 to 55 labelled b_1(2)* 54 to 14 labelled b_1(2)* 54 to 49 labelled b_1(2)* 55 to 56 labelled c_1(2)* 56 to 52 labelled b_1(2)* 56 to 53 labelled b_1(2)* 56 to 69 labelled b_1(3)* 69 to 70 labelled c_1(3)* 70 to 52 labelled b_1(3)* 70 to 53 labelled b_1(2)* 70 to 69 labelled b_1(3) 3.69/1.84 3.69/1.84 3.69/1.84 ---------------------------------------- 3.69/1.84 3.69/1.84 (2) 3.69/1.84 YES 3.69/1.87 EOF
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