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TRS Conditional pair #516978549
details
property
value
status
complete
benchmark
312.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n056.star.cs.uiowa.edu
space
COPS
run statistics
property
value
solver
AProVE21
configuration
standard
runtime (wallclock)
11.6274828911 seconds
cpu usage
12.897772245
max memory
1.091620864E9
stage attributes
key
value
output-size
11781
starexec-result
MAYBE
output
/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- MAYBE proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Quasi decreasingness of the given CTRS could not be shown: (0) CTRS (1) CTRSToQTRSProof [SOUND, 0 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 94 ms] (4) QTRS (5) DependencyPairsProof [EQUIVALENT, 13 ms] (6) QDP (7) DependencyGraphProof [EQUIVALENT, 0 ms] (8) AND (9) QDP (10) UsableRulesProof [EQUIVALENT, 0 ms] (11) QDP (12) QDPSizeChangeProof [EQUIVALENT, 0 ms] (13) YES (14) QDP (15) UsableRulesProof [EQUIVALENT, 0 ms] (16) QDP (17) TransformationProof [EQUIVALENT, 0 ms] (18) QDP (19) TransformationProof [EQUIVALENT, 0 ms] (20) QDP (21) MRRProof [EQUIVALENT, 12 ms] (22) QDP (23) TransformationProof [EQUIVALENT, 0 ms] (24) QDP (25) NonTerminationLoopProof [COMPLETE, 0 ms] (26) NO ---------------------------------------- (0) Obligation: Conditional term rewrite system: The TRS R consists of the following rules: gcd(x, 0) -> x gcd(0, x) -> x iadd(y) -> tp2(0, y) iadd(s(z)) -> u1(iadd(z)) u1(tp2(x, y)) -> tp2(s(x), y) iadd(add(x, y)) -> tp2(x, y) The conditional TRS C consists of the following conditional rules: gcd(z, y) -> gcd(x, y) <= iadd(z) -> tp2(x, y) gcd(y, z) -> gcd(x, y) <= iadd(z) -> tp2(x, y) ---------------------------------------- (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: gcd(z, y) -> U1(iadd(z), y) U1(tp2(x, y), y) -> gcd(x, y) gcd(y, z) -> U2(iadd(z), y) U2(tp2(x, y), y) -> gcd(x, y) gcd(x, 0) -> x gcd(0, x) -> x iadd(y) -> tp2(0, y) iadd(s(z)) -> u1(iadd(z)) u1(tp2(x, y)) -> tp2(s(x), y) iadd(add(x, y)) -> tp2(x, y) Q is empty. ---------------------------------------- (3) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(0) = 0 POL(U1(x_1, x_2)) = x_1 + x_2 POL(U2(x_1, x_2)) = x_1 + 2*x_2 POL(add(x_1, x_2)) = 1 + 2*x_1 + 2*x_2 POL(gcd(x_1, x_2)) = 1 + 2*x_1 + x_2 POL(iadd(x_1)) = 1 + x_1 POL(s(x_1)) = x_1 POL(tp2(x_1, x_2)) = 1 + 2*x_1 + x_2
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