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TRS Condi 20667 pair #381733087
details
property
value
status
complete
benchmark
354.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n049.star.cs.uiowa.edu
space
COPS
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.70437288284 seconds
cpu usage
3.665433853
max memory
1.92233472E8
stage attributes
key
value
output-size
2902
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Quasi decreasingness of the given CTRS could be proven: (0) CTRS (1) CTRSToQTRSProof [SOUND, 0 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 59 ms] (4) QTRS (5) QTRSRRRProof [EQUIVALENT, 0 ms] (6) QTRS (7) RisEmptyProof [EQUIVALENT, 0 ms] (8) YES ---------------------------------------- (0) Obligation: Conditional term rewrite system: The TRS R consists of the following rules: pos(s(0)) -> true pos(0) -> false The conditional TRS C consists of the following conditional rules: pos(s(x)) -> true <= pos(x) -> true pos(p(x)) -> false <= pos(x) -> false ---------------------------------------- (1) CTRSToQTRSProof (SOUND) The conditional rules have been transormed into unconditional rules according to [CTRS,AAECCNOC]. ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: pos(s(x)) -> U1(pos(x)) U1(true) -> true pos(p(x)) -> U2(pos(x)) U2(false) -> false pos(s(0)) -> true pos(0) -> false Q is empty. ---------------------------------------- (3) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(0) = 0 POL(U1(x_1)) = x_1 POL(U2(x_1)) = x_1 POL(false) = 1 POL(p(x_1)) = 1 + 2*x_1 POL(pos(x_1)) = 2 + 2*x_1 POL(s(x_1)) = x_1 POL(true) = 1 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: pos(p(x)) -> U2(pos(x)) pos(s(0)) -> true pos(0) -> false ---------------------------------------- (4) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: pos(s(x)) -> U1(pos(x)) U1(true) -> true U2(false) -> false Q is empty. ---------------------------------------- (5) QTRSRRRProof (EQUIVALENT) Used ordering:
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