Spaces
Explore
Communities
Statistics
Reports
Cluster
Status
Help
TRS Standard pair #516968190
details
property
value
status
complete
benchmark
t001.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n174.star.cs.uiowa.edu
space
HirokawaMiddeldorp_04
run statistics
property
value
solver
AProVE21
configuration
standard
runtime (wallclock)
2.67265486717 seconds
cpu usage
7.500091897
max memory
5.15977216E8
stage attributes
key
value
output-size
13949
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) DependencyPairsProof [EQUIVALENT, 0 ms] (2) QDP (3) DependencyGraphProof [EQUIVALENT, 0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) UsableRulesProof [EQUIVALENT, 0 ms] (17) QDP (18) QDPSizeChangeProof [EQUIVALENT, 0 ms] (19) YES (20) QDP (21) QDPOrderProof [EQUIVALENT, 7 ms] (22) QDP (23) QDPOrderProof [EQUIVALENT, 21 ms] (24) QDP (25) PisEmptyProof [EQUIVALENT, 0 ms] (26) YES (27) QDP (28) UsableRulesProof [EQUIVALENT, 0 ms] (29) QDP (30) QDPSizeChangeProof [EQUIVALENT, 0 ms] (31) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: -(x, 0) -> x -(s(x), s(y)) -> -(x, y) *(x, 0) -> 0 *(x, s(y)) -> +(*(x, y), x) if(true, x, y) -> x if(false, x, y) -> y odd(0) -> false odd(s(0)) -> true odd(s(s(x))) -> odd(x) half(0) -> 0 half(s(0)) -> 0 half(s(s(x))) -> s(half(x)) if(true, x, y) -> true if(false, x, y) -> false pow(x, y) -> f(x, y, s(0)) f(x, 0, z) -> z f(x, s(y), z) -> if(odd(s(y)), f(x, y, *(x, z)), f(*(x, x), half(s(y)), z)) 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: -^1(s(x), s(y)) -> -^1(x, y) *^1(x, s(y)) -> *^1(x, y) ODD(s(s(x))) -> ODD(x) HALF(s(s(x))) -> HALF(x) POW(x, y) -> F(x, y, s(0)) F(x, s(y), z) -> IF(odd(s(y)), f(x, y, *(x, z)), f(*(x, x), half(s(y)), z)) F(x, s(y), z) -> ODD(s(y)) F(x, s(y), z) -> F(x, y, *(x, z)) F(x, s(y), z) -> *^1(x, z) F(x, s(y), z) -> F(*(x, x), half(s(y)), z) F(x, s(y), z) -> *^1(x, x) F(x, s(y), z) -> HALF(s(y)) The TRS R consists of the following rules:
popout
output may be truncated. 'popout' for the full output.
job log
popout
actions
all output
return to TRS Standard