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TRS Standard pair #487073058
details
property
value
status
complete
benchmark
thiemann41.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n179.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
3.86265 seconds
cpu usage
5.24631
user time
5.01086
system time
0.235459
max virtual memory
3.6842316E7
max residence set size
338732.0
stage attributes
key
value
starexec-result
YES
output
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) Overlay + Local Confluence [EQUIVALENT, 6 ms] (2) QTRS (3) DependencyPairsProof [EQUIVALENT, 0 ms] (4) QDP (5) DependencyGraphProof [EQUIVALENT, 0 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) UsableRulesReductionPairsProof [EQUIVALENT, 0 ms] (20) QDP (21) PisEmptyProof [EQUIVALENT, 0 ms] (22) YES (23) QDP (24) UsableRulesProof [EQUIVALENT, 0 ms] (25) QDP (26) QReductionProof [EQUIVALENT, 0 ms] (27) QDP (28) NonInfProof [EQUIVALENT, 0 ms] (29) QDP (30) DependencyGraphProof [EQUIVALENT, 0 ms] (31) TRUE ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: times(x, y) -> sum(generate(x, y)) generate(x, y) -> gen(x, y, 0) gen(x, y, z) -> if(ge(z, x), x, y, z) if(true, x, y, z) -> nil if(false, x, y, z) -> cons(y, gen(x, y, s(z))) sum(nil) -> 0 sum(cons(0, xs)) -> sum(xs) sum(cons(s(x), xs)) -> s(sum(cons(x, xs))) ge(x, 0) -> true ge(0, s(y)) -> false ge(s(x), s(y)) -> ge(x, 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: times(x, y) -> sum(generate(x, y)) generate(x, y) -> gen(x, y, 0) gen(x, y, z) -> if(ge(z, x), x, y, z) if(true, x, y, z) -> nil if(false, x, y, z) -> cons(y, gen(x, y, s(z))) sum(nil) -> 0 sum(cons(0, xs)) -> sum(xs) sum(cons(s(x), xs)) -> s(sum(cons(x, xs))) ge(x, 0) -> true ge(0, s(y)) -> false ge(s(x), s(y)) -> ge(x, y) The set Q consists of the following terms: times(x0, x1) generate(x0, x1) gen(x0, x1, x2) if(true, x0, x1, x2) if(false, x0, x1, x2) sum(nil) sum(cons(0, x0)) sum(cons(s(x0), x1)) ge(x0, 0) ge(0, s(x0)) ge(s(x0), s(x1))
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