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TRS Innermost pair #487523991
details
property
value
status
complete
benchmark
#4.29.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n141.star.cs.uiowa.edu
space
AG01_innermost
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
2.09315299988 seconds
cpu usage
5.13795114
max memory
3.47705344E8
stage attributes
key
value
output-size
17539
starexec-result
YES
output
/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) DependencyPairsProof [EQUIVALENT, 0 ms] (2) QDP (3) DependencyGraphProof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) QReductionProof [EQUIVALENT, 0 ms] (9) QDP (10) QDPSizeChangeProof [EQUIVALENT, 0 ms] (11) YES (12) QDP (13) UsableRulesProof [EQUIVALENT, 0 ms] (14) QDP (15) QReductionProof [EQUIVALENT, 0 ms] (16) QDP (17) QDPSizeChangeProof [EQUIVALENT, 0 ms] (18) YES (19) QDP (20) UsableRulesProof [EQUIVALENT, 0 ms] (21) QDP (22) QReductionProof [EQUIVALENT, 0 ms] (23) QDP (24) QDPSizeChangeProof [EQUIVALENT, 0 ms] (25) YES (26) QDP (27) UsableRulesProof [EQUIVALENT, 0 ms] (28) QDP (29) QReductionProof [EQUIVALENT, 0 ms] (30) QDP (31) QDPOrderProof [EQUIVALENT, 0 ms] (32) QDP (33) QDPOrderProof [EQUIVALENT, 23 ms] (34) QDP (35) PisEmptyProof [EQUIVALENT, 0 ms] (36) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: even(0) -> true even(s(0)) -> false even(s(s(x))) -> even(x) half(0) -> 0 half(s(s(x))) -> s(half(x)) plus(0, y) -> y plus(s(x), y) -> s(plus(x, y)) times(0, y) -> 0 times(s(x), y) -> if_times(even(s(x)), s(x), y) if_times(true, s(x), y) -> plus(times(half(s(x)), y), times(half(s(x)), y)) if_times(false, s(x), y) -> plus(y, times(x, y)) The set Q consists of the following terms: even(0) even(s(0)) even(s(s(x0))) half(0) half(s(s(x0))) plus(0, x0) plus(s(x0), x1) times(0, x0) times(s(x0), x1) if_times(true, s(x0), x1) if_times(false, s(x0), x1) ---------------------------------------- (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: EVEN(s(s(x))) -> EVEN(x) HALF(s(s(x))) -> HALF(x) PLUS(s(x), y) -> PLUS(x, y)
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