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TRS Standard pair #516966460
details
property
value
status
complete
benchmark
4.60.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n083.star.cs.uiowa.edu
space
SK90
run statistics
property
value
solver
AProVE21
configuration
standard
runtime (wallclock)
2.39841413498 seconds
cpu usage
6.367771576
max memory
4.8340992E8
stage attributes
key
value
output-size
11875
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) Overlay + Local Confluence [EQUIVALENT, 0 ms] (2) QTRS (3) DependencyPairsProof [EQUIVALENT, 3 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) QDPOrderProof [EQUIVALENT, 3 ms] (27) QDP (28) PisEmptyProof [EQUIVALENT, 0 ms] (29) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: msort(nil) -> nil msort(.(x, y)) -> .(min(x, y), msort(del(min(x, y), .(x, y)))) min(x, nil) -> x min(x, .(y, z)) -> if(<=(x, y), min(x, z), min(y, z)) del(x, nil) -> nil del(x, .(y, z)) -> if(=(x, y), z, .(y, del(x, z))) 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: msort(nil) -> nil msort(.(x, y)) -> .(min(x, y), msort(del(min(x, y), .(x, y)))) min(x, nil) -> x min(x, .(y, z)) -> if(<=(x, y), min(x, z), min(y, z)) del(x, nil) -> nil del(x, .(y, z)) -> if(=(x, y), z, .(y, del(x, z))) The set Q consists of the following terms: msort(nil) msort(.(x0, x1)) min(x0, nil) min(x0, .(x1, x2)) del(x0, nil) del(x0, .(x1, x2)) ---------------------------------------- (3) DependencyPairsProof (EQUIVALENT) Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. ---------------------------------------- (4) Obligation: Q DP problem: The TRS P consists of the following rules:
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