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TRS Innermost pair #487524643
details
property
value
status
complete
benchmark
thiemann28i.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n079.star.cs.uiowa.edu
space
Mixed_innermost
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
3.44510102272 seconds
cpu usage
8.458804448
max memory
4.38419456E8
stage attributes
key
value
output-size
18342
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) DependencyPairsProof [EQUIVALENT, 0 ms] (2) QDP (3) DependencyGraphProof [EQUIVALENT, 3 ms] (4) AND (5) QDP (6) UsableRulesProof [EQUIVALENT, 0 ms] (7) QDP (8) QReductionProof [EQUIVALENT, 0 ms] (9) QDP (10) QDPSizeChangeProof [EQUIVALENT, 0 ms] (11) YES (12) QDP (13) UsableRulesProof [EQUIVALENT, 0 ms] (14) QDP (15) QReductionProof [EQUIVALENT, 0 ms] (16) QDP (17) QDPSizeChangeProof [EQUIVALENT, 0 ms] (18) YES (19) QDP (20) UsableRulesProof [EQUIVALENT, 0 ms] (21) QDP (22) QReductionProof [EQUIVALENT, 0 ms] (23) QDP (24) QDPQMonotonicMRRProof [EQUIVALENT, 17 ms] (25) QDP (26) QDPQMonotonicMRRProof [EQUIVALENT, 11 ms] (27) QDP (28) TransformationProof [SOUND, 0 ms] (29) QDP (30) TransformationProof [EQUIVALENT, 0 ms] (31) QDP (32) TransformationProof [SOUND, 0 ms] (33) QDP (34) TransformationProof [EQUIVALENT, 0 ms] (35) QDP (36) DependencyGraphProof [EQUIVALENT, 0 ms] (37) TRUE ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: ge(x, 0) -> true ge(0, s(y)) -> false ge(s(x), s(y)) -> ge(x, y) minus(x, 0) -> x minus(0, y) -> 0 minus(s(x), s(y)) -> minus(x, y) id_inc(x) -> x id_inc(x) -> s(x) div(x, y) -> if(ge(y, s(0)), ge(x, y), x, y) if(false, b, x, y) -> div_by_zero if(true, false, x, y) -> 0 if(true, true, x, y) -> id_inc(div(minus(x, y), y)) The set Q consists of the following terms: ge(x0, 0) ge(0, s(x0)) ge(s(x0), s(x1)) minus(x0, 0) minus(0, x0) minus(s(x0), s(x1)) id_inc(x0) div(x0, x1) if(false, x0, x1, x2) if(true, false, x0, x1) if(true, true, x0, x1) ---------------------------------------- (1) DependencyPairsProof (EQUIVALENT) Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. ---------------------------------------- (2) Obligation: Q DP problem: The TRS P consists of the following rules: GE(s(x), s(y)) -> GE(x, y)
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