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TRS Conditional pair #487562968
details
property
value
status
complete
benchmark
fib.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n054.star.cs.uiowa.edu
space
Mixed_CTRS
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.73219203949 seconds
cpu usage
3.921222867
max memory
2.38309376E8
stage attributes
key
value
output-size
8671
starexec-result
YES
output
/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox2/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Quasi decreasingness of the given CTRS could be proven: (0) CTRS (1) CTRSToQTRSProof [SOUND, 0 ms] (2) QTRS (3) Overlay + Local Confluence [EQUIVALENT, 0 ms] (4) QTRS (5) DependencyPairsProof [EQUIVALENT, 6 ms] (6) QDP (7) DependencyGraphProof [EQUIVALENT, 0 ms] (8) AND (9) QDP (10) UsableRulesProof [EQUIVALENT, 0 ms] (11) QDP (12) QReductionProof [EQUIVALENT, 0 ms] (13) QDP (14) QDPSizeChangeProof [EQUIVALENT, 0 ms] (15) YES (16) QDP (17) UsableRulesProof [EQUIVALENT, 0 ms] (18) QDP (19) QReductionProof [EQUIVALENT, 0 ms] (20) QDP (21) QDPSizeChangeProof [EQUIVALENT, 0 ms] (22) YES ---------------------------------------- (0) Obligation: Conditional term rewrite system: The TRS R consists of the following rules: fib(0) -> pair(0, s(0)) The conditional TRS C consists of the following conditional rules: plus(x, y) -> y' <= x -> 0, y -> y' plus(x, y) -> s(plus(x', y')) <= x -> s(x'), y -> y' fib(s(x)) -> pair(z, plus(y, z)) <= fib(x) -> pair(y, z) ---------------------------------------- (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: plus(x, y) -> U1(x, y) U1(s(x'), y) -> U3(y, x') U3(y', x') -> s(plus(x', y')) U1(0, y) -> U2(y) U2(y') -> y' fib(s(x)) -> U4(fib(x)) U4(pair(y, z)) -> pair(z, plus(y, z)) fib(0) -> pair(0, s(0)) Q is empty. ---------------------------------------- (3) Overlay + Local Confluence (EQUIVALENT) The TRS is overlay and locally confluent. By [NOC] we can switch to innermost. ---------------------------------------- (4) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: plus(x, y) -> U1(x, y) U1(s(x'), y) -> U3(y, x') U3(y', x') -> s(plus(x', y')) U1(0, y) -> U2(y) U2(y') -> y' fib(s(x)) -> U4(fib(x)) U4(pair(y, z)) -> pair(z, plus(y, z)) fib(0) -> pair(0, s(0)) The set Q consists of the following terms: plus(x0, x1) U1(s(x0), x1)
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