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TRS Standard pair #516964681
details
property
value
status
complete
benchmark
bn122.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n055.star.cs.uiowa.edu
space
Rubio_04
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
0.101670980453 seconds
cpu usage
0.036803708
max memory
2871296.0
stage attributes
key
value
output-size
2713
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 Z:S) (RULES plus(plus(X:S,Y:S),Z:S) -> plus(X:S,plus(Y:S,Z:S)) times(X:S,s(Y:S)) -> plus(X:S,times(Y:S,X:S)) ) Problem 1: Dependency Pairs Processor: -> Pairs: PLUS(plus(X:S,Y:S),Z:S) -> PLUS(X:S,plus(Y:S,Z:S)) PLUS(plus(X:S,Y:S),Z:S) -> PLUS(Y:S,Z:S) TIMES(X:S,s(Y:S)) -> PLUS(X:S,times(Y:S,X:S)) TIMES(X:S,s(Y:S)) -> TIMES(Y:S,X:S) -> Rules: plus(plus(X:S,Y:S),Z:S) -> plus(X:S,plus(Y:S,Z:S)) times(X:S,s(Y:S)) -> plus(X:S,times(Y:S,X:S)) Problem 1: SCC Processor: -> Pairs: PLUS(plus(X:S,Y:S),Z:S) -> PLUS(X:S,plus(Y:S,Z:S)) PLUS(plus(X:S,Y:S),Z:S) -> PLUS(Y:S,Z:S) TIMES(X:S,s(Y:S)) -> PLUS(X:S,times(Y:S,X:S)) TIMES(X:S,s(Y:S)) -> TIMES(Y:S,X:S) -> Rules: plus(plus(X:S,Y:S),Z:S) -> plus(X:S,plus(Y:S,Z:S)) times(X:S,s(Y:S)) -> plus(X:S,times(Y:S,X:S)) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: PLUS(plus(X:S,Y:S),Z:S) -> PLUS(X:S,plus(Y:S,Z:S)) PLUS(plus(X:S,Y:S),Z:S) -> PLUS(Y:S,Z:S) ->->-> Rules: plus(plus(X:S,Y:S),Z:S) -> plus(X:S,plus(Y:S,Z:S)) times(X:S,s(Y:S)) -> plus(X:S,times(Y:S,X:S)) ->->Cycle: ->->-> Pairs: TIMES(X:S,s(Y:S)) -> TIMES(Y:S,X:S) ->->-> Rules: plus(plus(X:S,Y:S),Z:S) -> plus(X:S,plus(Y:S,Z:S)) times(X:S,s(Y:S)) -> plus(X:S,times(Y:S,X:S)) The problem is decomposed in 2 subproblems. Problem 1.1: Subterm Processor: -> Pairs: PLUS(plus(X:S,Y:S),Z:S) -> PLUS(X:S,plus(Y:S,Z:S)) PLUS(plus(X:S,Y:S),Z:S) -> PLUS(Y:S,Z:S) -> Rules: plus(plus(X:S,Y:S),Z:S) -> plus(X:S,plus(Y:S,Z:S)) times(X:S,s(Y:S)) -> plus(X:S,times(Y:S,X:S)) ->Projection: pi(PLUS) = 1 Problem 1.1: SCC Processor: -> Pairs: Empty -> Rules: plus(plus(X:S,Y:S),Z:S) -> plus(X:S,plus(Y:S,Z:S)) times(X:S,s(Y:S)) -> plus(X:S,times(Y:S,X:S)) ->Strongly Connected Components: There is no strongly connected component The problem is finite. Problem 1.2: Reduction Pair Processor: -> Pairs: TIMES(X:S,s(Y:S)) -> TIMES(Y:S,X:S) -> Rules: plus(plus(X:S,Y:S),Z:S) -> plus(X:S,plus(Y:S,Z:S)) times(X:S,s(Y:S)) -> plus(X:S,times(Y:S,X:S)) -> Usable rules: Empty ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2
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