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SRS_Relative 2019-03-29 08.12 pair #432296558
details
property
value
status
complete
benchmark
random-86.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n018.star.cs.uiowa.edu
space
Waldmann_19
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
11.9096 seconds
cpu usage
43.5627
user time
41.7006
system time
1.86204
max virtual memory
4.0101384E7
max residence set size
4109552.0
stage attributes
key
value
starexec-result
YES
output
43.39/11.85 YES 43.39/11.87 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 43.39/11.87 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 43.39/11.87 43.39/11.87 43.39/11.87 Termination of the given RelTRS could be proven: 43.39/11.87 43.39/11.87 (0) RelTRS 43.39/11.87 (1) RelTRSRRRProof [EQUIVALENT, 1094 ms] 43.39/11.87 (2) RelTRS 43.39/11.87 (3) RelTRSRRRProof [EQUIVALENT, 31 ms] 43.39/11.87 (4) RelTRS 43.39/11.87 (5) SIsEmptyProof [EQUIVALENT, 0 ms] 43.39/11.87 (6) QTRS 43.39/11.87 (7) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms] 43.39/11.87 (8) YES 43.39/11.87 43.39/11.87 43.39/11.87 ---------------------------------------- 43.39/11.87 43.39/11.87 (0) 43.39/11.87 Obligation: 43.39/11.87 Relative term rewrite system: 43.39/11.87 The relative TRS consists of the following R rules: 43.39/11.87 43.39/11.87 c(c(a(x1))) -> b(a(c(x1))) 43.39/11.87 b(b(b(x1))) -> a(a(a(x1))) 43.39/11.87 43.39/11.87 The relative TRS consists of the following S rules: 43.39/11.87 43.39/11.87 c(a(b(x1))) -> a(a(a(x1))) 43.39/11.87 c(a(b(x1))) -> a(c(a(x1))) 43.39/11.87 c(b(c(x1))) -> c(b(b(x1))) 43.39/11.87 b(a(b(x1))) -> b(b(c(x1))) 43.39/11.87 43.39/11.87 43.39/11.87 ---------------------------------------- 43.39/11.87 43.39/11.87 (1) RelTRSRRRProof (EQUIVALENT) 43.39/11.87 We used the following monotonic ordering for rule removal: 43.39/11.87 Matrix interpretation [MATRO] to (N^6, +, *, >=, >) : 43.39/11.87 43.39/11.87 <<< 43.39/11.87 POL(c(x_1)) = [[1], [1], [0], [0], [0], [1]] + [[1, 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, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0]] * x_1 43.39/11.87 >>> 43.39/11.87 43.39/11.87 <<< 43.39/11.87 POL(a(x_1)) = [[0], [0], [0], [0], [0], [0]] + [[1, 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, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0]] * x_1 43.39/11.87 >>> 43.39/11.87 43.39/11.87 <<< 43.39/11.87 POL(b(x_1)) = [[0], [1], [0], [0], [0], [0]] + [[1, 0, 1, 0, 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, 0, 0]] * x_1 43.39/11.87 >>> 43.39/11.87 43.39/11.87 With this ordering the following rules can be removed [MATRO] because they are oriented strictly: 43.39/11.87 Rules from R: 43.39/11.87 none 43.39/11.87 Rules from S: 43.39/11.87 43.39/11.87 c(a(b(x1))) -> a(a(a(x1))) 43.39/11.87 c(b(c(x1))) -> c(b(b(x1))) 43.39/11.87 43.39/11.87 43.39/11.87 43.39/11.87 43.39/11.87 ---------------------------------------- 43.39/11.87 43.39/11.87 (2) 43.39/11.87 Obligation: 43.39/11.87 Relative term rewrite system: 43.39/11.87 The relative TRS consists of the following R rules: 43.39/11.87 43.39/11.87 c(c(a(x1))) -> b(a(c(x1))) 43.39/11.87 b(b(b(x1))) -> a(a(a(x1))) 43.39/11.87 43.39/11.87 The relative TRS consists of the following S rules: 43.39/11.87 43.39/11.87 c(a(b(x1))) -> a(c(a(x1))) 43.39/11.87 b(a(b(x1))) -> b(b(c(x1))) 43.39/11.87 43.39/11.87 43.39/11.87 ---------------------------------------- 43.39/11.87 43.39/11.87 (3) RelTRSRRRProof (EQUIVALENT) 43.39/11.87 We used the following monotonic ordering for rule removal: 43.39/11.87 Matrix interpretation [MATRO] to (N^2, +, *, >=, >) : 43.39/11.87 43.39/11.87 <<< 43.39/11.87 POL(c(x_1)) = [[0], [1]] + [[2, 0], [1, 0]] * x_1 43.39/11.87 >>> 43.39/11.87 43.39/11.87 <<< 43.39/11.87 POL(a(x_1)) = [[1], [2]] + [[2, 0], [0, 0]] * x_1 43.39/11.87 >>> 43.39/11.87 43.39/11.87 <<< 43.39/11.87 POL(b(x_1)) = [[1], [2]] + [[2, 0], [0, 0]] * x_1 43.39/11.87 >>> 43.39/11.87 43.39/11.87 With this ordering the following rules can be removed [MATRO] because they are oriented strictly:
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