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TRS Conditional pair #487562936
details
property
value
status
complete
benchmark
353.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n146.star.cs.uiowa.edu
space
COPS
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
2.15645813942 seconds
cpu usage
5.52748021
max memory
3.47578368E8
stage attributes
key
value
output-size
15629
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Quasi decreasingness of the given CTRS could be proven: (0) CTRS (1) CTRSToQTRSProof [SOUND, 0 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 60 ms] (4) QTRS (5) QTRSRRRProof [EQUIVALENT, 13 ms] (6) QTRS (7) QTRSRRRProof [EQUIVALENT, 21 ms] (8) QTRS (9) QTRSRRRProof [EQUIVALENT, 23 ms] (10) QTRS (11) DependencyPairsProof [EQUIVALENT, 0 ms] (12) QDP (13) DependencyGraphProof [EQUIVALENT, 0 ms] (14) AND (15) QDP (16) UsableRulesProof [EQUIVALENT, 0 ms] (17) QDP (18) QDPSizeChangeProof [EQUIVALENT, 0 ms] (19) YES (20) QDP (21) UsableRulesReductionPairsProof [EQUIVALENT, 0 ms] (22) QDP (23) MRRProof [EQUIVALENT, 0 ms] (24) QDP (25) DependencyGraphProof [EQUIVALENT, 0 ms] (26) TRUE ---------------------------------------- (0) Obligation: Conditional term rewrite system: The TRS R consists of the following rules: ssp'(xs, 0) -> nil sub(z, 0) -> z get(cons(y, ys)) -> tp2(y, ys) The conditional TRS C consists of the following conditional rules: ssp'(cons(y', ws), v) -> cons(y', ys') <= sub(v, y') -> w, ssp'(ws, w) -> ys' ssp'(cons(x', xs'), v) -> cons(y', ys') <= get(xs') -> tp2(y', zs), sub(v, y') -> w, ssp'(cons(x', zs), w) -> ys' sub(s(v), s(w)) -> z <= sub(v, w) -> z get(cons(x', xs')) -> tp2(y, cons(x', zs)) <= get(xs') -> tp2(y, zs) ---------------------------------------- (1) CTRSToQTRSProof (SOUND) The conditional rules have been transormed into unconditional rules according to [CTRS,AAECCNOC]. ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: ssp'(cons(y', ws), v) -> U1(sub(v, y'), y', ws) U1(w, y', ws) -> U2(ssp'(ws, w), y') U2(ys', y') -> cons(y', ys') ssp'(cons(x', xs'), v) -> U3(get(xs'), x', v) U3(tp2(y', zs), x', v) -> U4(sub(v, y'), x', y', zs) U4(w, x', y', zs) -> U5(ssp'(cons(x', zs), w), y') U5(ys', y') -> cons(y', ys') sub(s(v), s(w)) -> U6(sub(v, w)) U6(z) -> z get(cons(x', xs')) -> U7(get(xs'), x') U7(tp2(y, zs), x') -> tp2(y, cons(x', zs)) ssp'(xs, 0) -> nil sub(z, 0) -> z get(cons(y, ys)) -> tp2(y, ys) Q is empty. ---------------------------------------- (3) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(0) = 0 POL(U1(x_1, x_2, x_3)) = x_1 + x_2 + 2*x_3 POL(U2(x_1, x_2)) = x_1 + x_2 POL(U3(x_1, x_2, x_3)) = 2*x_1 + 2*x_2 + x_3 POL(U4(x_1, x_2, x_3, x_4)) = x_1 + 2*x_2 + x_3 + 2*x_4
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