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TRS Standard pair #516960941
details
property
value
status
complete
benchmark
thiemann16.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n004.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
3.70010900497 seconds
cpu usage
3.433566865
max memory
1.9771392E7
stage attributes
key
value
output-size
19825
starexec-result
YES
output
/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES Problem 1: (VAR v_NonEmpty:S u:S x:S y:S z:S) (RULES check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(x:S)))) -> check(s(x:S)) half(0) -> 0 half(s(0)) -> 0 half(s(s(x:S))) -> s(half(x:S)) if(even,x:S,y:S,z:S,u:S) -> plus(timesIter(half(x:S),y:S,half(z:S)),timesIter(half(x:S),y:S,half(s(z:S)))) if(odd,x:S,y:S,z:S,u:S) -> timesIter(p(x:S),y:S,u:S) if(zero,x:S,y:S,z:S,u:S) -> z:S p(0) -> 0 p(s(x:S)) -> x:S plus(0,y:S) -> y:S plus(s(x:S),y:S) -> s(plus(x:S,y:S)) times(x:S,y:S) -> timesIter(x:S,y:S,0) timesIter(x:S,y:S,z:S) -> if(check(x:S),x:S,y:S,z:S,plus(z:S,y:S)) ) Problem 1: Innermost Equivalent Processor: -> Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(x:S)))) -> check(s(x:S)) half(0) -> 0 half(s(0)) -> 0 half(s(s(x:S))) -> s(half(x:S)) if(even,x:S,y:S,z:S,u:S) -> plus(timesIter(half(x:S),y:S,half(z:S)),timesIter(half(x:S),y:S,half(s(z:S)))) if(odd,x:S,y:S,z:S,u:S) -> timesIter(p(x:S),y:S,u:S) if(zero,x:S,y:S,z:S,u:S) -> z:S p(0) -> 0 p(s(x:S)) -> x:S plus(0,y:S) -> y:S plus(s(x:S),y:S) -> s(plus(x:S,y:S)) times(x:S,y:S) -> timesIter(x:S,y:S,0) timesIter(x:S,y:S,z:S) -> if(check(x:S),x:S,y:S,z:S,plus(z:S,y:S)) -> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination. Problem 1: Dependency Pairs Processor: -> Pairs: CHECK(s(s(s(x:S)))) -> CHECK(s(x:S)) HALF(s(s(x:S))) -> HALF(x:S) IF(even,x:S,y:S,z:S,u:S) -> HALF(s(z:S)) IF(even,x:S,y:S,z:S,u:S) -> HALF(x:S) IF(even,x:S,y:S,z:S,u:S) -> HALF(z:S) IF(even,x:S,y:S,z:S,u:S) -> PLUS(timesIter(half(x:S),y:S,half(z:S)),timesIter(half(x:S),y:S,half(s(z:S)))) IF(even,x:S,y:S,z:S,u:S) -> TIMESITER(half(x:S),y:S,half(s(z:S))) IF(even,x:S,y:S,z:S,u:S) -> TIMESITER(half(x:S),y:S,half(z:S)) IF(odd,x:S,y:S,z:S,u:S) -> P(x:S) IF(odd,x:S,y:S,z:S,u:S) -> TIMESITER(p(x:S),y:S,u:S) PLUS(s(x:S),y:S) -> PLUS(x:S,y:S) TIMES(x:S,y:S) -> TIMESITER(x:S,y:S,0) TIMESITER(x:S,y:S,z:S) -> CHECK(x:S) TIMESITER(x:S,y:S,z:S) -> IF(check(x:S),x:S,y:S,z:S,plus(z:S,y:S)) TIMESITER(x:S,y:S,z:S) -> PLUS(z:S,y:S) -> Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(x:S)))) -> check(s(x:S)) half(0) -> 0 half(s(0)) -> 0 half(s(s(x:S))) -> s(half(x:S)) if(even,x:S,y:S,z:S,u:S) -> plus(timesIter(half(x:S),y:S,half(z:S)),timesIter(half(x:S),y:S,half(s(z:S)))) if(odd,x:S,y:S,z:S,u:S) -> timesIter(p(x:S),y:S,u:S) if(zero,x:S,y:S,z:S,u:S) -> z:S p(0) -> 0 p(s(x:S)) -> x:S plus(0,y:S) -> y:S plus(s(x:S),y:S) -> s(plus(x:S,y:S)) times(x:S,y:S) -> timesIter(x:S,y:S,0) timesIter(x:S,y:S,z:S) -> if(check(x:S),x:S,y:S,z:S,plus(z:S,y:S)) Problem 1: SCC Processor: -> Pairs: CHECK(s(s(s(x:S)))) -> CHECK(s(x:S)) HALF(s(s(x:S))) -> HALF(x:S) IF(even,x:S,y:S,z:S,u:S) -> HALF(s(z:S)) IF(even,x:S,y:S,z:S,u:S) -> HALF(x:S) IF(even,x:S,y:S,z:S,u:S) -> HALF(z:S) IF(even,x:S,y:S,z:S,u:S) -> PLUS(timesIter(half(x:S),y:S,half(z:S)),timesIter(half(x:S),y:S,half(s(z:S))))
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