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TRS Conditional pair #487562962
details
property
value
status
complete
benchmark
quotrem.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n141.star.cs.uiowa.edu
space
Mixed_CTRS
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.87362098694 seconds
cpu usage
4.321582129
max memory
2.55541248E8
stage attributes
key
value
output-size
14923
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Quasi decreasingness of the given CTRS could be proven: (0) CTRS (1) CTRSToQTRSProof [SOUND, 0 ms] (2) QTRS (3) Overlay + Local Confluence [EQUIVALENT, 0 ms] (4) QTRS (5) DependencyPairsProof [EQUIVALENT, 0 ms] (6) QDP (7) DependencyGraphProof [EQUIVALENT, 0 ms] (8) AND (9) QDP (10) UsableRulesProof [EQUIVALENT, 0 ms] (11) QDP (12) QReductionProof [EQUIVALENT, 0 ms] (13) QDP (14) QDPSizeChangeProof [EQUIVALENT, 0 ms] (15) YES (16) QDP (17) UsableRulesProof [EQUIVALENT, 0 ms] (18) QDP (19) QReductionProof [EQUIVALENT, 0 ms] (20) QDP (21) QDPSizeChangeProof [EQUIVALENT, 0 ms] (22) YES (23) QDP (24) UsableRulesProof [EQUIVALENT, 0 ms] (25) QDP (26) QReductionProof [EQUIVALENT, 0 ms] (27) QDP (28) QDPOrderProof [EQUIVALENT, 0 ms] (29) QDP (30) DependencyGraphProof [EQUIVALENT, 0 ms] (31) TRUE ---------------------------------------- (0) Obligation: Conditional term rewrite system: The TRS R consists of the following rules: less(x, 0) -> false less(0, s(x)) -> true less(s(x), s(y)) -> less(x, y) minus(0, s(y)) -> 0 minus(x, 0) -> x minus(s(x), s(y)) -> minus(x, y) quotrem(0, s(y)) -> pair(0, 0) The conditional TRS C consists of the following conditional rules: quotrem(s(x), s(y)) -> pair(0, s(x)) <= less(x, y) -> true quotrem(s(x), s(y)) -> pair(s(q), r) <= less(x, y) -> false, quotrem(minus(x, y), s(y)) -> pair(q, r) ---------------------------------------- (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: quotrem(s(x), s(y)) -> U1(less(x, y), x, y) U1(true, x, y) -> pair(0, s(x)) U1(false, x, y) -> U2(quotrem(minus(x, y), s(y))) U2(pair(q, r)) -> pair(s(q), r) less(x, 0) -> false less(0, s(x)) -> true less(s(x), s(y)) -> less(x, y) minus(0, s(y)) -> 0 minus(x, 0) -> x minus(s(x), s(y)) -> minus(x, y) quotrem(0, s(y)) -> pair(0, 0) Q is empty. ---------------------------------------- (3) Overlay + Local Confluence (EQUIVALENT) The TRS is overlay and locally confluent. By [NOC] we can switch to innermost. ---------------------------------------- (4)
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