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TRS Conditional pair #516978557
details
property
value
status
complete
benchmark
411.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n082.star.cs.uiowa.edu
space
COPS
run statistics
property
value
solver
AProVE21
configuration
standard
runtime (wallclock)
2.66787004471 seconds
cpu usage
6.726779
max memory
6.27666944E8
stage attributes
key
value
output-size
4670
starexec-result
MAYBE
output
/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- MAYBE proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Quasi decreasingness of the given CTRS could not be shown: (0) CTRS (1) CTRSToQTRSProof [SOUND, 0 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 30 ms] (4) QTRS (5) AAECC Innermost [EQUIVALENT, 0 ms] (6) QTRS (7) DependencyPairsProof [EQUIVALENT, 0 ms] (8) QDP (9) UsableRulesProof [EQUIVALENT, 0 ms] (10) QDP (11) QReductionProof [EQUIVALENT, 0 ms] (12) QDP (13) NonTerminationLoopProof [COMPLETE, 0 ms] (14) NO ---------------------------------------- (0) Obligation: Conditional term rewrite system: The TRS R consists of the following rules: g(s(x)) -> x h(s(x)) -> x a -> d b -> d e -> e The conditional TRS C consists of the following conditional rules: f(x, y) -> g(x) <= a -> d f(x, y) -> h(x) <= b -> d ---------------------------------------- (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: f(x, y) -> U1(a, x) U1(d, x) -> g(x) f(x, y) -> U2(b, x) U2(d, x) -> h(x) g(s(x)) -> x h(s(x)) -> x a -> d b -> d e -> e Q is empty. ---------------------------------------- (3) QTRSRRRProof (EQUIVALENT) Used ordering: Knuth-Bendix order [KBO] with precedence:b > f_2 > U2_2 > g_1 > d > a > U1_2 > e > s_1 > h_1 and weight map: a=2 d=1 b=2 e=1 g_1=1 h_1=1 s_1=1 f_2=2 U1_2=1 U2_2=1 The variable weight is 1With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: f(x, y) -> U1(a, x) U1(d, x) -> g(x) f(x, y) -> U2(b, x) U2(d, x) -> h(x) g(s(x)) -> x h(s(x)) -> x a -> d
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