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TRS Standard pair #516964641
details
property
value
status
complete
benchmark
quotminus.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n045.star.cs.uiowa.edu
space
Rubio_04
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
0.104253053665 seconds
cpu usage
0.043707605
max memory
3477504.0
stage attributes
key
value
output-size
5270
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 min(min(X:S,Y:S),Z) -> min(X:S,plus(Y:S,Z)) min(s(X:S),s(Y:S)) -> min(X:S,Y:S) min(X:S,0) -> X:S plus(0,Y:S) -> Y:S plus(s(X:S),Y:S) -> s(plus(X:S,Y:S)) quot(0,s(Y:S)) -> 0 quot(s(X:S),s(Y:S)) -> s(quot(min(X:S,Y:S),s(Y:S))) ) Problem 1: Dependency Pairs Processor: -> Pairs: MIN(min(X:S,Y:S),Z) -> MIN(X:S,plus(Y:S,Z)) MIN(min(X:S,Y:S),Z) -> PLUS(Y:S,Z) MIN(s(X:S),s(Y:S)) -> MIN(X:S,Y:S) PLUS(s(X:S),Y:S) -> PLUS(X:S,Y:S) QUOT(s(X:S),s(Y:S)) -> MIN(X:S,Y:S) QUOT(s(X:S),s(Y:S)) -> QUOT(min(X:S,Y:S),s(Y:S)) -> Rules: min(min(X:S,Y:S),Z) -> min(X:S,plus(Y:S,Z)) min(s(X:S),s(Y:S)) -> min(X:S,Y:S) min(X:S,0) -> X:S plus(0,Y:S) -> Y:S plus(s(X:S),Y:S) -> s(plus(X:S,Y:S)) quot(0,s(Y:S)) -> 0 quot(s(X:S),s(Y:S)) -> s(quot(min(X:S,Y:S),s(Y:S))) Problem 1: SCC Processor: -> Pairs: MIN(min(X:S,Y:S),Z) -> MIN(X:S,plus(Y:S,Z)) MIN(min(X:S,Y:S),Z) -> PLUS(Y:S,Z) MIN(s(X:S),s(Y:S)) -> MIN(X:S,Y:S) PLUS(s(X:S),Y:S) -> PLUS(X:S,Y:S) QUOT(s(X:S),s(Y:S)) -> MIN(X:S,Y:S) QUOT(s(X:S),s(Y:S)) -> QUOT(min(X:S,Y:S),s(Y:S)) -> Rules: min(min(X:S,Y:S),Z) -> min(X:S,plus(Y:S,Z)) min(s(X:S),s(Y:S)) -> min(X:S,Y:S) min(X:S,0) -> X:S plus(0,Y:S) -> Y:S plus(s(X:S),Y:S) -> s(plus(X:S,Y:S)) quot(0,s(Y:S)) -> 0 quot(s(X:S),s(Y:S)) -> s(quot(min(X:S,Y:S),s(Y:S))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: PLUS(s(X:S),Y:S) -> PLUS(X:S,Y:S) ->->-> Rules: min(min(X:S,Y:S),Z) -> min(X:S,plus(Y:S,Z)) min(s(X:S),s(Y:S)) -> min(X:S,Y:S) min(X:S,0) -> X:S plus(0,Y:S) -> Y:S plus(s(X:S),Y:S) -> s(plus(X:S,Y:S)) quot(0,s(Y:S)) -> 0 quot(s(X:S),s(Y:S)) -> s(quot(min(X:S,Y:S),s(Y:S))) ->->Cycle: ->->-> Pairs: MIN(min(X:S,Y:S),Z) -> MIN(X:S,plus(Y:S,Z)) MIN(s(X:S),s(Y:S)) -> MIN(X:S,Y:S) ->->-> Rules: min(min(X:S,Y:S),Z) -> min(X:S,plus(Y:S,Z)) min(s(X:S),s(Y:S)) -> min(X:S,Y:S) min(X:S,0) -> X:S plus(0,Y:S) -> Y:S plus(s(X:S),Y:S) -> s(plus(X:S,Y:S)) quot(0,s(Y:S)) -> 0 quot(s(X:S),s(Y:S)) -> s(quot(min(X:S,Y:S),s(Y:S))) ->->Cycle: ->->-> Pairs: QUOT(s(X:S),s(Y:S)) -> QUOT(min(X:S,Y:S),s(Y:S)) ->->-> Rules: min(min(X:S,Y:S),Z) -> min(X:S,plus(Y:S,Z)) min(s(X:S),s(Y:S)) -> min(X:S,Y:S) min(X:S,0) -> X:S plus(0,Y:S) -> Y:S plus(s(X:S),Y:S) -> s(plus(X:S,Y:S)) quot(0,s(Y:S)) -> 0 quot(s(X:S),s(Y:S)) -> s(quot(min(X:S,Y:S),s(Y:S))) The problem is decomposed in 3 subproblems. Problem 1.1: Subterm Processor:
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