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SRS Stand 10685 pair #381718743
details
property
value
status
complete
benchmark
dup16.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n079.star.cs.uiowa.edu
space
Trafo_06
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
2.16256999969 seconds
cpu usage
5.45697923
max memory
3.70597888E8
stage attributes
key
value
output-size
2781
starexec-result
YES
output
/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRS Reverse [EQUIVALENT, 0 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 4 ms] (4) QTRS (5) QTRSRRRProof [EQUIVALENT, 0 ms] (6) QTRS (7) RisEmptyProof [EQUIVALENT, 0 ms] (8) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a(a(a(a(x1)))) -> b(b(b(b(b(b(x1)))))) b(b(b(b(x1)))) -> c(c(c(c(c(c(x1)))))) c(c(c(c(x1)))) -> d(d(d(d(d(d(x1)))))) b(b(x1)) -> d(d(d(d(x1)))) c(c(d(d(d(d(x1)))))) -> a(a(x1)) Q is empty. ---------------------------------------- (1) QTRS Reverse (EQUIVALENT) We applied the QTRS Reverse Processor [REVERSE]. ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a(a(a(a(x1)))) -> b(b(b(b(b(b(x1)))))) b(b(b(b(x1)))) -> c(c(c(c(c(c(x1)))))) c(c(c(c(x1)))) -> d(d(d(d(d(d(x1)))))) b(b(x1)) -> d(d(d(d(x1)))) d(d(d(d(c(c(x1)))))) -> a(a(x1)) Q is empty. ---------------------------------------- (3) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(a(x_1)) = 66 + x_1 POL(b(x_1)) = 44 + x_1 POL(c(x_1)) = 29 + x_1 POL(d(x_1)) = 19 + x_1 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: b(b(b(b(x1)))) -> c(c(c(c(c(c(x1)))))) c(c(c(c(x1)))) -> d(d(d(d(d(d(x1)))))) b(b(x1)) -> d(d(d(d(x1)))) d(d(d(d(c(c(x1)))))) -> a(a(x1)) ---------------------------------------- (4) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a(a(a(a(x1)))) -> b(b(b(b(b(b(x1)))))) Q is empty. ---------------------------------------- (5) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(a(x_1)) = 1 + x_1 POL(b(x_1)) = x_1 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: a(a(a(a(x1)))) -> b(b(b(b(b(b(x1))))))
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