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TRS Standard pair #516964746
details
property
value
status
complete
benchmark
gm.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n065.star.cs.uiowa.edu
space
Rubio_04
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
0.0562260150909 seconds
cpu usage
0.040850627
max memory
3489792.0
stage attributes
key
value
output-size
3649
starexec-result
YES
output
/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES Problem 1: (VAR v_NonEmpty:S X:S Y:S) (RULES div(0,s(Y:S)) -> 0 div(s(X:S),s(Y:S)) -> s(div(minus(X:S,Y:S),s(Y:S))) minus(s(X:S),s(Y:S)) -> p(minus(X:S,Y:S)) minus(X:S,0) -> X:S p(s(X:S)) -> X:S ) Problem 1: Innermost Equivalent Processor: -> Rules: div(0,s(Y:S)) -> 0 div(s(X:S),s(Y:S)) -> s(div(minus(X:S,Y:S),s(Y:S))) minus(s(X:S),s(Y:S)) -> p(minus(X:S,Y:S)) minus(X:S,0) -> X:S 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: DIV(s(X:S),s(Y:S)) -> DIV(minus(X:S,Y:S),s(Y:S)) DIV(s(X:S),s(Y:S)) -> MINUS(X:S,Y:S) MINUS(s(X:S),s(Y:S)) -> MINUS(X:S,Y:S) MINUS(s(X:S),s(Y:S)) -> P(minus(X:S,Y:S)) -> Rules: div(0,s(Y:S)) -> 0 div(s(X:S),s(Y:S)) -> s(div(minus(X:S,Y:S),s(Y:S))) minus(s(X:S),s(Y:S)) -> p(minus(X:S,Y:S)) minus(X:S,0) -> X:S p(s(X:S)) -> X:S Problem 1: SCC Processor: -> Pairs: DIV(s(X:S),s(Y:S)) -> DIV(minus(X:S,Y:S),s(Y:S)) DIV(s(X:S),s(Y:S)) -> MINUS(X:S,Y:S) MINUS(s(X:S),s(Y:S)) -> MINUS(X:S,Y:S) MINUS(s(X:S),s(Y:S)) -> P(minus(X:S,Y:S)) -> Rules: div(0,s(Y:S)) -> 0 div(s(X:S),s(Y:S)) -> s(div(minus(X:S,Y:S),s(Y:S))) minus(s(X:S),s(Y:S)) -> p(minus(X:S,Y:S)) minus(X:S,0) -> X:S p(s(X:S)) -> X:S ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: MINUS(s(X:S),s(Y:S)) -> MINUS(X:S,Y:S) ->->-> Rules: div(0,s(Y:S)) -> 0 div(s(X:S),s(Y:S)) -> s(div(minus(X:S,Y:S),s(Y:S))) minus(s(X:S),s(Y:S)) -> p(minus(X:S,Y:S)) minus(X:S,0) -> X:S p(s(X:S)) -> X:S ->->Cycle: ->->-> Pairs: DIV(s(X:S),s(Y:S)) -> DIV(minus(X:S,Y:S),s(Y:S)) ->->-> Rules: div(0,s(Y:S)) -> 0 div(s(X:S),s(Y:S)) -> s(div(minus(X:S,Y:S),s(Y:S))) minus(s(X:S),s(Y:S)) -> p(minus(X:S,Y:S)) minus(X:S,0) -> X:S p(s(X:S)) -> X:S The problem is decomposed in 2 subproblems. Problem 1.1: Subterm Processor: -> Pairs: MINUS(s(X:S),s(Y:S)) -> MINUS(X:S,Y:S) -> Rules: div(0,s(Y:S)) -> 0 div(s(X:S),s(Y:S)) -> s(div(minus(X:S,Y:S),s(Y:S))) minus(s(X:S),s(Y:S)) -> p(minus(X:S,Y:S)) minus(X:S,0) -> X:S p(s(X:S)) -> X:S ->Projection: pi(MINUS) = 1 Problem 1.1: SCC Processor:
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