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TRS Stand 20472 pair #381711784
details
property
value
status
complete
benchmark
logarquot.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n030.star.cs.uiowa.edu
space
Rubio_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.72087192535 seconds
cpu usage
3.995841699
max memory
2.56913408E8
stage attributes
key
value
output-size
12220
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) Overlay + Local Confluence [EQUIVALENT, 0 ms] (2) QTRS (3) DependencyPairsProof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, 22 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) QDPOrderProof [EQUIVALENT, 0 ms] (20) QDP (21) PisEmptyProof [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) PisEmptyProof [EQUIVALENT, 0 ms] (31) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: min(X, 0) -> X min(s(X), s(Y)) -> min(X, Y) quot(0, s(Y)) -> 0 quot(s(X), s(Y)) -> s(quot(min(X, Y), s(Y))) log(s(0)) -> 0 log(s(s(X))) -> s(log(s(quot(X, s(s(0)))))) 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: min(X, 0) -> X min(s(X), s(Y)) -> min(X, Y) quot(0, s(Y)) -> 0 quot(s(X), s(Y)) -> s(quot(min(X, Y), s(Y))) log(s(0)) -> 0 log(s(s(X))) -> s(log(s(quot(X, s(s(0)))))) The set Q consists of the following terms: min(x0, 0) min(s(x0), s(x1)) quot(0, s(x0)) quot(s(x0), s(x1)) log(s(0)) log(s(s(x0))) ---------------------------------------- (3) DependencyPairsProof (EQUIVALENT) Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. ---------------------------------------- (4) Obligation: Q DP problem:
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