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TRS Conditional pair #516978551
details
property
value
status
complete
benchmark
315.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n139.star.cs.uiowa.edu
space
COPS
run statistics
property
value
solver
AProVE21
configuration
standard
runtime (wallclock)
2.14771199226 seconds
cpu usage
5.577405671
max memory
4.71764992E8
stage attributes
key
value
output-size
3163
starexec-result
YES
output
/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox2/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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Quasi decreasingness of the given CTRS could be proven: (0) CTRS (1) CTRSToQTRSProof [SOUND, 0 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 79 ms] (4) QTRS (5)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: g(d, x, x) -> A h(x, x) -> g(x, x, f(k)) a -> c a -> d b -> c b -> d c -> e c -> l k -> l k -> m d -> m The conditional TRS C consists of the following conditional rules: f(x) -> x <= x -> e ---------------------------------------- (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) -> U1(x, x) U1(e, x) -> x g(d, x, x) -> A h(x, x) -> g(x, x, f(k)) a -> c a -> d b -> c b -> d c -> e c -> l k -> l k -> m d -> m Q is empty. ---------------------------------------- (3) QTRSRRRProof (EQUIVALENT) Used ordering: Quasi precedence: a > c > e a > c > [h_2, k, l] > f_1 > U1_2 a > c > [h_2, k, l] > g_3 > A a > c > [h_2, k, l] > [d, m] b > c > e b > c > [h_2, k, l] > f_1 > U1_2 b > c > [h_2, k, l] > g_3 > A b > c > [h_2, k, l] > [d, m] Status: f_1: multiset status U1_2: [1,2] e: multiset status g_3: [2,1,3] d: multiset status A: multiset status h_2: multiset status k: multiset status a: multiset status
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