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TRS Standard pair #516964650
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
n170.star.cs.uiowa.edu
space
Rubio_04
run statistics
property
value
solver
AProVE21
configuration
standard
runtime (wallclock)
2.38744997978 seconds
cpu usage
6.385292061
max memory
4.84368384E8
stage attributes
key
value
output-size
13745
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) Overlay + Local Confluence [EQUIVALENT, 0 ms] (2) QTRS (3) DependencyPairsProof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, 0 ms] (4) QDP (5) DependencyGraphProof [EQUIVALENT, 4 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, 42 ms] (27) QDP (28) PisEmptyProof [EQUIVALENT, 0 ms] (29) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: le(0, Y) -> true le(s(X), 0) -> false le(s(X), s(Y)) -> le(X, Y) minus(0, Y) -> 0 minus(s(X), Y) -> ifMinus(le(s(X), Y), s(X), Y) ifMinus(true, s(X), Y) -> 0 ifMinus(false, s(X), Y) -> s(minus(X, Y)) quot(0, s(Y)) -> 0 quot(s(X), s(Y)) -> s(quot(minus(X, Y), s(Y))) 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: le(0, Y) -> true le(s(X), 0) -> false le(s(X), s(Y)) -> le(X, Y) minus(0, Y) -> 0 minus(s(X), Y) -> ifMinus(le(s(X), Y), s(X), Y) ifMinus(true, s(X), Y) -> 0 ifMinus(false, s(X), Y) -> s(minus(X, Y)) quot(0, s(Y)) -> 0 quot(s(X), s(Y)) -> s(quot(minus(X, Y), s(Y))) The set Q consists of the following terms: le(0, x0) le(s(x0), 0) le(s(x0), s(x1)) minus(0, x0) minus(s(x0), x1) ifMinus(true, s(x0), x1) ifMinus(false, s(x0), x1) quot(0, s(x0)) quot(s(x0), s(x1)) ----------------------------------------
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