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TRS Standard pair #516966916
details
property
value
status
complete
benchmark
2.25.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n183.star.cs.uiowa.edu
space
SK90
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
0.0773260593414 seconds
cpu usage
0.020360383
max memory
1765376.0
stage attributes
key
value
output-size
2917
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 +(x:S,0) -> x:S +(x:S,s(y:S)) -> s(+(x:S,y:S)) fib(0) -> 0 fib(s(0)) -> s(0) fib(s(s(x:S))) -> +(fib(s(x:S)),fib(x:S)) ) Problem 1: Innermost Equivalent Processor: -> Rules: +(x:S,0) -> x:S +(x:S,s(y:S)) -> s(+(x:S,y:S)) fib(0) -> 0 fib(s(0)) -> s(0) fib(s(s(x:S))) -> +(fib(s(x:S)),fib(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: +#(x:S,s(y:S)) -> +#(x:S,y:S) FIB(s(s(x:S))) -> +#(fib(s(x:S)),fib(x:S)) FIB(s(s(x:S))) -> FIB(s(x:S)) FIB(s(s(x:S))) -> FIB(x:S) -> Rules: +(x:S,0) -> x:S +(x:S,s(y:S)) -> s(+(x:S,y:S)) fib(0) -> 0 fib(s(0)) -> s(0) fib(s(s(x:S))) -> +(fib(s(x:S)),fib(x:S)) Problem 1: SCC Processor: -> Pairs: +#(x:S,s(y:S)) -> +#(x:S,y:S) FIB(s(s(x:S))) -> +#(fib(s(x:S)),fib(x:S)) FIB(s(s(x:S))) -> FIB(s(x:S)) FIB(s(s(x:S))) -> FIB(x:S) -> Rules: +(x:S,0) -> x:S +(x:S,s(y:S)) -> s(+(x:S,y:S)) fib(0) -> 0 fib(s(0)) -> s(0) fib(s(s(x:S))) -> +(fib(s(x:S)),fib(x:S)) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: +#(x:S,s(y:S)) -> +#(x:S,y:S) ->->-> Rules: +(x:S,0) -> x:S +(x:S,s(y:S)) -> s(+(x:S,y:S)) fib(0) -> 0 fib(s(0)) -> s(0) fib(s(s(x:S))) -> +(fib(s(x:S)),fib(x:S)) ->->Cycle: ->->-> Pairs: FIB(s(s(x:S))) -> FIB(s(x:S)) FIB(s(s(x:S))) -> FIB(x:S) ->->-> Rules: +(x:S,0) -> x:S +(x:S,s(y:S)) -> s(+(x:S,y:S)) fib(0) -> 0 fib(s(0)) -> s(0) fib(s(s(x:S))) -> +(fib(s(x:S)),fib(x:S)) The problem is decomposed in 2 subproblems. Problem 1.1: Subterm Processor: -> Pairs: +#(x:S,s(y:S)) -> +#(x:S,y:S) -> Rules: +(x:S,0) -> x:S +(x:S,s(y:S)) -> s(+(x:S,y:S)) fib(0) -> 0 fib(s(0)) -> s(0) fib(s(s(x:S))) -> +(fib(s(x:S)),fib(x:S)) ->Projection: pi(+#) = 2 Problem 1.1:
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