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TRS Standard pair #516963905
details
property
value
status
complete
benchmark
fac.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n060.star.cs.uiowa.edu
space
AProVE_04
run statistics
property
value
solver
AProVE21
configuration
standard
runtime (wallclock)
2.55872488022 seconds
cpu usage
6.91377321
max memory
5.2045824E8
stage attributes
key
value
output-size
16289
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) DependencyPairsProof [EQUIVALENT, 0 ms] (2) QDP (3) DependencyGraphProof [EQUIVALENT, 0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) MNOCProof [EQUIVALENT, 0 ms] (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) MNOCProof [EQUIVALENT, 0 ms] (16) QDP (17) UsableRulesProof [EQUIVALENT, 0 ms] (18) QDP (19) QReductionProof [EQUIVALENT, 0 ms] (20) QDP (21) QDPSizeChangeProof [EQUIVALENT, 0 ms] (22) YES (23) QDP (24) MNOCProof [EQUIVALENT, 0 ms] (25) QDP (26) UsableRulesProof [EQUIVALENT, 0 ms] (27) QDP (28) QReductionProof [EQUIVALENT, 0 ms] (29) QDP (30) QDPSizeChangeProof [EQUIVALENT, 0 ms] (31) YES (32) QDP (33) MNOCProof [EQUIVALENT, 0 ms] (34) QDP (35) UsableRulesProof [EQUIVALENT, 0 ms] (36) QDP (37) QReductionProof [EQUIVALENT, 0 ms] (38) QDP (39) MRRProof [EQUIVALENT, 9 ms] (40) QDP (41) QDPOrderProof [EQUIVALENT, 15 ms] (42) QDP (43) PisEmptyProof [EQUIVALENT, 0 ms] (44) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: plus(x, 0) -> x plus(x, s(y)) -> s(plus(x, y)) times(0, y) -> 0 times(x, 0) -> 0 times(s(x), y) -> plus(times(x, y), y) p(s(s(x))) -> s(p(s(x))) p(s(0)) -> 0 fac(s(x)) -> times(fac(p(s(x))), s(x)) Q is empty. ---------------------------------------- (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: PLUS(x, s(y)) -> PLUS(x, y) TIMES(s(x), y) -> PLUS(times(x, y), y) TIMES(s(x), y) -> TIMES(x, y) P(s(s(x))) -> P(s(x)) FAC(s(x)) -> TIMES(fac(p(s(x))), s(x)) FAC(s(x)) -> FAC(p(s(x))) FAC(s(x)) -> P(s(x)) The TRS R consists of the following rules: plus(x, 0) -> x
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