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TRS_Relative 2019-03-21 03.54 pair #429988602
details
property
value
status
complete
benchmark
#3.35_rand.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n118.star.cs.uiowa.edu
space
INVY_15
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
2.62735 seconds
cpu usage
6.88085
user time
6.50875
system time
0.372107
max virtual memory
1.9475168E7
max residence set size
681344.0
stage attributes
key
value
starexec-result
YES
output
6.80/2.59 YES 6.80/2.60 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 6.80/2.60 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 6.80/2.60 6.80/2.60 6.80/2.60 Termination of the given RelTRS could be proven: 6.80/2.60 6.80/2.60 (0) RelTRS 6.80/2.60 (1) RelTRS Reverse [SOUND, 0 ms] 6.80/2.60 (2) RelTRS 6.80/2.60 (3) RelTRSRRRProof [EQUIVALENT, 21 ms] 6.80/2.60 (4) RelTRS 6.80/2.60 (5) RelTRSRRRProof [EQUIVALENT, 5 ms] 6.80/2.60 (6) RelTRS 6.80/2.60 (7) RelTRSRRRProof [EQUIVALENT, 0 ms] 6.80/2.60 (8) RelTRS 6.80/2.60 (9) RIsEmptyProof [EQUIVALENT, 0 ms] 6.80/2.60 (10) YES 6.80/2.60 6.80/2.60 6.80/2.60 ---------------------------------------- 6.80/2.60 6.80/2.60 (0) 6.80/2.60 Obligation: 6.80/2.60 Relative term rewrite system: 6.80/2.60 The relative TRS consists of the following R rules: 6.80/2.60 6.80/2.60 g(s(x)) -> f(x) 6.80/2.60 f(0) -> s(0) 6.80/2.60 f(s(x)) -> s(s(g(x))) 6.80/2.60 g(0) -> 0 6.80/2.60 6.80/2.60 The relative TRS consists of the following S rules: 6.80/2.60 6.80/2.60 rand(x) -> x 6.80/2.60 rand(x) -> rand(s(x)) 6.80/2.60 6.80/2.60 6.80/2.60 ---------------------------------------- 6.80/2.60 6.80/2.60 (1) RelTRS Reverse (SOUND) 6.80/2.60 We have reversed the following relative TRS [REVERSE]: 6.80/2.60 The set of rules R is 6.80/2.60 g(s(x)) -> f(x) 6.80/2.60 f(0) -> s(0) 6.80/2.60 f(s(x)) -> s(s(g(x))) 6.80/2.60 g(0) -> 0 6.80/2.60 6.80/2.60 The set of rules S is 6.80/2.60 rand(x) -> x 6.80/2.60 rand(x) -> rand(s(x)) 6.80/2.60 6.80/2.60 We have obtained the following relative TRS: 6.80/2.60 The set of rules R is 6.80/2.60 s(g(x)) -> f(x) 6.80/2.60 0'(f(x)) -> 0'(s(x)) 6.80/2.60 s(f(x)) -> g(s(s(x))) 6.80/2.60 0'(g(x)) -> 0'(x) 6.80/2.60 6.80/2.60 The set of rules S is 6.80/2.60 rand(x) -> x 6.80/2.60 rand(x) -> s(rand(x)) 6.80/2.60 6.80/2.60 6.80/2.60 ---------------------------------------- 6.80/2.60 6.80/2.60 (2) 6.80/2.60 Obligation: 6.80/2.60 Relative term rewrite system: 6.80/2.60 The relative TRS consists of the following R rules: 6.80/2.60 6.80/2.60 s(g(x)) -> f(x) 6.80/2.60 0'(f(x)) -> 0'(s(x)) 6.80/2.60 s(f(x)) -> g(s(s(x))) 6.80/2.60 0'(g(x)) -> 0'(x) 6.80/2.60 6.80/2.60 The relative TRS consists of the following S rules: 6.80/2.60 6.80/2.60 rand(x) -> x 6.80/2.60 rand(x) -> s(rand(x)) 6.80/2.60 6.80/2.60 6.80/2.60 ---------------------------------------- 6.80/2.60 6.80/2.60 (3) RelTRSRRRProof (EQUIVALENT) 6.80/2.60 We used the following monotonic ordering for rule removal: 6.80/2.60 Polynomial interpretation [POLO]: 6.80/2.60 6.80/2.60 POL(0'(x_1)) = x_1 6.80/2.60 POL(f(x_1)) = x_1 6.80/2.60 POL(g(x_1)) = x_1 6.80/2.60 POL(rand(x_1)) = 1 + x_1 6.80/2.60 POL(s(x_1)) = x_1 6.80/2.60 With this ordering the following rules can be removed [MATRO] because they are oriented strictly: 6.80/2.60 Rules from R: 6.80/2.60 none 6.80/2.60 Rules from S: 6.80/2.60 6.80/2.60 rand(x) -> x 6.80/2.60
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