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TRS Stand 20472 pair #381709971
details
property
value
status
complete
benchmark
division.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n026.star.cs.uiowa.edu
space
Secret_06_TRS
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
3.6312520504 seconds
cpu usage
9.070481956
max memory
4.45681664E8
stage attributes
key
value
output-size
20024
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) Overlay + Local Confluence [EQUIVALENT, 7 ms] (2) QTRS (3) DependencyPairsProof [EQUIVALENT, 0 ms] (4) QDP (5) DependencyGraphProof [EQUIVALENT, 0 ms] (6) AND (7) QDP (8) UsableRulesProof [EQUIVALENT, 0 ms] (9) QDP (10) QReductionProof [EQUIVALENT, 0 ms] (11) QDP (12) QDPSizeChangeProof [EQUIVALENT, 0 ms] (13) YES (14) QDP (15) UsableRulesProof [EQUIVALENT, 0 ms] (16) QDP (17) QReductionProof [EQUIVALENT, 0 ms] (18) QDP (19) QDPSizeChangeProof [EQUIVALENT, 0 ms] (20) YES (21) QDP (22) UsableRulesProof [EQUIVALENT, 0 ms] (23) QDP (24) QReductionProof [EQUIVALENT, 0 ms] (25) QDP (26) QDPSizeChangeProof [EQUIVALENT, 0 ms] (27) YES (28) QDP (29) UsableRulesProof [EQUIVALENT, 0 ms] (30) QDP (31) QReductionProof [EQUIVALENT, 0 ms] (32) QDP (33) TransformationProof [EQUIVALENT, 0 ms] (34) QDP (35) DependencyGraphProof [EQUIVALENT, 0 ms] (36) QDP (37) TransformationProof [EQUIVALENT, 0 ms] (38) QDP (39) QDPOrderProof [EQUIVALENT, 0 ms] (40) QDP (41) DependencyGraphProof [EQUIVALENT, 0 ms] (42) TRUE ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: division(x, y) -> div(x, y, 0) div(x, y, z) -> if(lt(x, y), x, y, inc(z)) if(true, x, y, z) -> z if(false, x, s(y), z) -> div(minus(x, s(y)), s(y), z) minus(x, 0) -> x minus(s(x), s(y)) -> minus(x, y) lt(x, 0) -> false lt(0, s(y)) -> true lt(s(x), s(y)) -> lt(x, y) inc(0) -> s(0) inc(s(x)) -> s(inc(x)) Q is empty. ---------------------------------------- (1) Overlay + Local Confluence (EQUIVALENT) The TRS is overlay and locally confluent. By [NOC] we can switch to innermost. ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: division(x, y) -> div(x, y, 0) div(x, y, z) -> if(lt(x, y), x, y, inc(z)) if(true, x, y, z) -> z if(false, x, s(y), z) -> div(minus(x, s(y)), s(y), z) minus(x, 0) -> x minus(s(x), s(y)) -> minus(x, y) lt(x, 0) -> false lt(0, s(y)) -> true lt(s(x), s(y)) -> lt(x, y) inc(0) -> s(0)
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