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TRS Stand 20472 pair #381713608
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
n029.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
2.27639818192 seconds
cpu usage
5.241286516
max memory
2.80481792E8
stage attributes
key
value
output-size
17227
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) Overlay + Local Confluence [EQUIVALENT, 2 ms] (2) QTRS (3) DependencyPairsProof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, 7 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))
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