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TRS Stand 20472 pair #381714289
details
property
value
status
complete
benchmark
2.29.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n105.star.cs.uiowa.edu
space
SK90
run statistics
property
value
solver
muterm 5.18
configuration
default
runtime (wallclock)
0.0184509754181 seconds
cpu usage
0.0150493
max memory
1630208.0
stage attributes
key
value
output-size
2716
starexec-result
YES
output
/export/starexec/sandbox/solver/bin/starexec_run_default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES Problem 1: (VAR x y) (RULES divp(x,y) -> =(rem(x,y),0) prime(0) -> false prime(s(0)) -> false prime(s(s(x))) -> prime1(s(s(x)),s(x)) prime1(x,0) -> false prime1(x,s(0)) -> true prime1(x,s(s(y))) -> and(not(divp(s(s(y)),x)),prime1(x,s(y))) ) Problem 1: Innermost Equivalent Processor: -> Rules: divp(x,y) -> =(rem(x,y),0) prime(0) -> false prime(s(0)) -> false prime(s(s(x))) -> prime1(s(s(x)),s(x)) prime1(x,0) -> false prime1(x,s(0)) -> true prime1(x,s(s(y))) -> and(not(divp(s(s(y)),x)),prime1(x,s(y))) -> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination. Problem 1: Dependency Pairs Processor: -> Pairs: PRIME(s(s(x))) -> PRIME1(s(s(x)),s(x)) PRIME1(x,s(s(y))) -> DIVP(s(s(y)),x) PRIME1(x,s(s(y))) -> PRIME1(x,s(y)) -> Rules: divp(x,y) -> =(rem(x,y),0) prime(0) -> false prime(s(0)) -> false prime(s(s(x))) -> prime1(s(s(x)),s(x)) prime1(x,0) -> false prime1(x,s(0)) -> true prime1(x,s(s(y))) -> and(not(divp(s(s(y)),x)),prime1(x,s(y))) Problem 1: SCC Processor: -> Pairs: PRIME(s(s(x))) -> PRIME1(s(s(x)),s(x)) PRIME1(x,s(s(y))) -> DIVP(s(s(y)),x) PRIME1(x,s(s(y))) -> PRIME1(x,s(y)) -> Rules: divp(x,y) -> =(rem(x,y),0) prime(0) -> false prime(s(0)) -> false prime(s(s(x))) -> prime1(s(s(x)),s(x)) prime1(x,0) -> false prime1(x,s(0)) -> true prime1(x,s(s(y))) -> and(not(divp(s(s(y)),x)),prime1(x,s(y))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: PRIME1(x,s(s(y))) -> PRIME1(x,s(y)) ->->-> Rules: divp(x,y) -> =(rem(x,y),0) prime(0) -> false prime(s(0)) -> false prime(s(s(x))) -> prime1(s(s(x)),s(x)) prime1(x,0) -> false prime1(x,s(0)) -> true prime1(x,s(s(y))) -> and(not(divp(s(s(y)),x)),prime1(x,s(y))) Problem 1: Subterm Processor: -> Pairs: PRIME1(x,s(s(y))) -> PRIME1(x,s(y)) -> Rules: divp(x,y) -> =(rem(x,y),0) prime(0) -> false prime(s(0)) -> false prime(s(s(x))) -> prime1(s(s(x)),s(x)) prime1(x,0) -> false prime1(x,s(0)) -> true prime1(x,s(s(y))) -> and(not(divp(s(s(y)),x)),prime1(x,s(y))) ->Projection: pi(PRIME1) = 2 Problem 1: SCC Processor: -> Pairs: Empty
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