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TRS Conditional pair #516978493
details
property
value
status
complete
benchmark
plus1.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n032.star.cs.uiowa.edu
space
Mixed_CTRS_2014
run statistics
property
value
solver
AProVE21
configuration
standard
runtime (wallclock)
2.07834291458 seconds
cpu usage
5.410982534
max memory
4.80821248E8
stage attributes
key
value
output-size
2040
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Quasi decreasingness of the given CTRS could be proven: (0) CTRS (1) CTRSToQTRSProof [SOUND, 0 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 28 ms] (4) QTRS (5) RisEmptyProof [EQUIVALENT, 0 ms] (6) YES ---------------------------------------- (0) Obligation: Conditional term rewrite system: The TRS R consists of the following rules: plus(x, 0) -> x plus(0, x) -> x The conditional TRS C consists of the following conditional rules: plus(s(x), y) -> s(z) <= plus(x, y) -> z ---------------------------------------- (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: plus(s(x), y) -> U1(plus(x, y)) U1(z) -> s(z) plus(x, 0) -> x plus(0, x) -> x Q is empty. ---------------------------------------- (3) QTRSRRRProof (EQUIVALENT) Used ordering: Knuth-Bendix order [KBO] with precedence:0 > plus_2 > U1_1 > s_1 and weight map: 0=1 s_1=1 U1_1=1 plus_2=0 The variable weight is 1With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: plus(s(x), y) -> U1(plus(x, y)) U1(z) -> s(z) plus(x, 0) -> x plus(0, x) -> x ---------------------------------------- (4) Obligation: Q restricted rewrite system: R is empty. Q is empty. ---------------------------------------- (5) RisEmptyProof (EQUIVALENT) The TRS R is empty. Hence, termination is trivially proven. ---------------------------------------- (6) YES
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