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TRS Standard pair #516964281
details
property
value
status
complete
benchmark
7.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n178.star.cs.uiowa.edu
space
Beerendonk_07
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
0.111530065536 seconds
cpu usage
0.062262128
max memory
3731456.0
stage attributes
key
value
output-size
3567
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 v_NonEmpty:S x:S) (RULES cond(ttrue,x:S) -> cond(odd(x:S),p(p(p(x:S)))) odd(0) -> ffalse odd(s(0)) -> ttrue odd(s(s(x:S))) -> odd(x:S) p(0) -> 0 p(s(x:S)) -> x:S ) Problem 1: Innermost Equivalent Processor: -> Rules: cond(ttrue,x:S) -> cond(odd(x:S),p(p(p(x:S)))) odd(0) -> ffalse odd(s(0)) -> ttrue odd(s(s(x:S))) -> odd(x:S) p(0) -> 0 p(s(x:S)) -> x:S -> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination. Problem 1: Dependency Pairs Processor: -> Pairs: COND(ttrue,x:S) -> COND(odd(x:S),p(p(p(x:S)))) COND(ttrue,x:S) -> ODD(x:S) COND(ttrue,x:S) -> P(p(p(x:S))) COND(ttrue,x:S) -> P(p(x:S)) COND(ttrue,x:S) -> P(x:S) ODD(s(s(x:S))) -> ODD(x:S) -> Rules: cond(ttrue,x:S) -> cond(odd(x:S),p(p(p(x:S)))) odd(0) -> ffalse odd(s(0)) -> ttrue odd(s(s(x:S))) -> odd(x:S) p(0) -> 0 p(s(x:S)) -> x:S Problem 1: SCC Processor: -> Pairs: COND(ttrue,x:S) -> COND(odd(x:S),p(p(p(x:S)))) COND(ttrue,x:S) -> ODD(x:S) COND(ttrue,x:S) -> P(p(p(x:S))) COND(ttrue,x:S) -> P(p(x:S)) COND(ttrue,x:S) -> P(x:S) ODD(s(s(x:S))) -> ODD(x:S) -> Rules: cond(ttrue,x:S) -> cond(odd(x:S),p(p(p(x:S)))) odd(0) -> ffalse odd(s(0)) -> ttrue odd(s(s(x:S))) -> odd(x:S) p(0) -> 0 p(s(x:S)) -> x:S ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ODD(s(s(x:S))) -> ODD(x:S) ->->-> Rules: cond(ttrue,x:S) -> cond(odd(x:S),p(p(p(x:S)))) odd(0) -> ffalse odd(s(0)) -> ttrue odd(s(s(x:S))) -> odd(x:S) p(0) -> 0 p(s(x:S)) -> x:S ->->Cycle: ->->-> Pairs: COND(ttrue,x:S) -> COND(odd(x:S),p(p(p(x:S)))) ->->-> Rules: cond(ttrue,x:S) -> cond(odd(x:S),p(p(p(x:S)))) odd(0) -> ffalse odd(s(0)) -> ttrue odd(s(s(x:S))) -> odd(x:S) p(0) -> 0 p(s(x:S)) -> x:S The problem is decomposed in 2 subproblems. Problem 1.1: Subterm Processor: -> Pairs: ODD(s(s(x:S))) -> ODD(x:S) -> Rules: cond(ttrue,x:S) -> cond(odd(x:S),p(p(p(x:S))))
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