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TRS Standard pair #516963995
details
property
value
status
complete
benchmark
10.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n142.star.cs.uiowa.edu
space
Various_04
run statistics
property
value
solver
AProVE21
configuration
standard
runtime (wallclock)
2.60155200958 seconds
cpu usage
6.888242869
max memory
5.29330176E8
stage attributes
key
value
output-size
21902
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) DependencyPairsProof [EQUIVALENT, 0 ms] (2) QDP (3) DependencyGraphProof [EQUIVALENT, 0 ms] (4) AND (5) QDP (6) UsableRulesProof [EQUIVALENT, 0 ms] (7) QDP (8) QDPSizeChangeProof [EQUIVALENT, 0 ms] (9) YES (10) QDP (11) UsableRulesProof [EQUIVALENT, 0 ms] (12) QDP (13) QDPSizeChangeProof [EQUIVALENT, 0 ms] (14) YES (15) QDP (16) QDPOrderProof [EQUIVALENT, 0 ms] (17) QDP (18) PisEmptyProof [EQUIVALENT, 0 ms] (19) YES (20) QDP (21) UsableRulesProof [EQUIVALENT, 0 ms] (22) QDP (23) QDPSizeChangeProof [EQUIVALENT, 0 ms] (24) YES (25) QDP (26) UsableRulesProof [EQUIVALENT, 0 ms] (27) QDP (28) QDPSizeChangeProof [EQUIVALENT, 0 ms] (29) YES (30) QDP (31) UsableRulesProof [EQUIVALENT, 0 ms] (32) QDP (33) MNOCProof [EQUIVALENT, 0 ms] (34) QDP (35) UsableRulesReductionPairsProof [EQUIVALENT, 0 ms] (36) QDP (37) PisEmptyProof [EQUIVALENT, 0 ms] (38) YES (39) QDP (40) UsableRulesProof [EQUIVALENT, 0 ms] (41) QDP (42) UsableRulesReductionPairsProof [EQUIVALENT, 0 ms] (43) QDP (44) MRRProof [EQUIVALENT, 0 ms] (45) QDP (46) MRRProof [EQUIVALENT, 15 ms] (47) QDP (48) DependencyGraphProof [EQUIVALENT, 0 ms] (49) TRUE ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: +(0, y) -> y +(s(x), y) -> s(+(x, y)) ++(nil, ys) -> ys ++(:(x, xs), ys) -> :(x, ++(xs, ys)) sum(:(x, nil)) -> :(x, nil) sum(:(x, :(y, xs))) -> sum(:(+(x, y), xs)) sum(++(xs, :(x, :(y, ys)))) -> sum(++(xs, sum(:(x, :(y, ys))))) -(x, 0) -> x -(0, s(y)) -> 0 -(s(x), s(y)) -> -(x, y) quot(0, s(y)) -> 0 quot(s(x), s(y)) -> s(quot(-(x, y), s(y))) length(nil) -> 0 length(:(x, xs)) -> s(length(xs)) hd(:(x, xs)) -> x avg(xs) -> quot(hd(sum(xs)), length(xs)) Q is empty. ---------------------------------------- (1) DependencyPairsProof (EQUIVALENT) Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. ---------------------------------------- (2) Obligation: Q DP problem:
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