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TRS Standard pair #516966611
details
property
value
status
complete
benchmark
2.31.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n175.star.cs.uiowa.edu
space
SK90
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
0.0832209587097 seconds
cpu usage
0.020291517
max memory
1630208.0
stage attributes
key
value
output-size
3812
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 y:S) (RULES +(s(x:S),y:S) -> s(+(x:S,y:S)) +(x:S,0) -> x:S +(x:S,s(y:S)) -> s(+(x:S,y:S)) not(ffalse) -> ttrue not(ttrue) -> ffalse odd(0) -> ffalse odd(s(x:S)) -> not(odd(x:S)) ) Problem 1: Dependency Pairs Processor: -> Pairs: +#(s(x:S),y:S) -> +#(x:S,y:S) +#(x:S,s(y:S)) -> +#(x:S,y:S) ODD(s(x:S)) -> NOT(odd(x:S)) ODD(s(x:S)) -> ODD(x:S) -> Rules: +(s(x:S),y:S) -> s(+(x:S,y:S)) +(x:S,0) -> x:S +(x:S,s(y:S)) -> s(+(x:S,y:S)) not(ffalse) -> ttrue not(ttrue) -> ffalse odd(0) -> ffalse odd(s(x:S)) -> not(odd(x:S)) Problem 1: SCC Processor: -> Pairs: +#(s(x:S),y:S) -> +#(x:S,y:S) +#(x:S,s(y:S)) -> +#(x:S,y:S) ODD(s(x:S)) -> NOT(odd(x:S)) ODD(s(x:S)) -> ODD(x:S) -> Rules: +(s(x:S),y:S) -> s(+(x:S,y:S)) +(x:S,0) -> x:S +(x:S,s(y:S)) -> s(+(x:S,y:S)) not(ffalse) -> ttrue not(ttrue) -> ffalse odd(0) -> ffalse odd(s(x:S)) -> not(odd(x:S)) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ODD(s(x:S)) -> ODD(x:S) ->->-> Rules: +(s(x:S),y:S) -> s(+(x:S,y:S)) +(x:S,0) -> x:S +(x:S,s(y:S)) -> s(+(x:S,y:S)) not(ffalse) -> ttrue not(ttrue) -> ffalse odd(0) -> ffalse odd(s(x:S)) -> not(odd(x:S)) ->->Cycle: ->->-> Pairs: +#(s(x:S),y:S) -> +#(x:S,y:S) +#(x:S,s(y:S)) -> +#(x:S,y:S) ->->-> Rules: +(s(x:S),y:S) -> s(+(x:S,y:S)) +(x:S,0) -> x:S +(x:S,s(y:S)) -> s(+(x:S,y:S)) not(ffalse) -> ttrue not(ttrue) -> ffalse odd(0) -> ffalse odd(s(x:S)) -> not(odd(x:S)) The problem is decomposed in 2 subproblems. Problem 1.1: Subterm Processor: -> Pairs: ODD(s(x:S)) -> ODD(x:S) -> Rules: +(s(x:S),y:S) -> s(+(x:S,y:S)) +(x:S,0) -> x:S +(x:S,s(y:S)) -> s(+(x:S,y:S)) not(ffalse) -> ttrue not(ttrue) -> ffalse odd(0) -> ffalse odd(s(x:S)) -> not(odd(x:S)) ->Projection: pi(ODD) = 1 Problem 1.1:
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