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TRS Standard pair #516964691
details
property
value
status
complete
benchmark
enno.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
Rubio_04
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
0.173837184906 seconds
cpu usage
0.099681419
max memory
5005312.0
stage attributes
key
value
output-size
16844
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 M:S N:S X:S Y:S Z:S) (RULES append(add(N:S,X:S),Y:S) -> add(N:S,append(X:S,Y:S)) append(nil,Y:S) -> Y:S f_1(pair(X:S,Z:S),N:S,M:S,Y:S) -> f_2(lt(N:S,M:S),N:S,M:S,Y:S,X:S,Z:S) f_2(ffalse,N:S,M:S,Y:S,X:S,Z:S) -> pair(add(M:S,X:S),Z:S) f_2(ttrue,N:S,M:S,Y:S,X:S,Z:S) -> pair(X:S,add(M:S,Z:S)) f_3(pair(Y:S,Z:S),N:S,X:S) -> append(qsort(Y:S),add(X:S,qsort(Z:S))) lt(0,s(X:S)) -> ttrue lt(s(X:S),0) -> ffalse lt(s(X:S),s(Y:S)) -> lt(X:S,Y:S) qsort(add(N:S,X:S)) -> f_3(split(N:S,X:S),N:S,X:S) qsort(nil) -> nil split(N:S,add(M:S,Y:S)) -> f_1(split(N:S,Y:S),N:S,M:S,Y:S) split(N:S,nil) -> pair(nil,nil) ) Problem 1: Innermost Equivalent Processor: -> Rules: append(add(N:S,X:S),Y:S) -> add(N:S,append(X:S,Y:S)) append(nil,Y:S) -> Y:S f_1(pair(X:S,Z:S),N:S,M:S,Y:S) -> f_2(lt(N:S,M:S),N:S,M:S,Y:S,X:S,Z:S) f_2(ffalse,N:S,M:S,Y:S,X:S,Z:S) -> pair(add(M:S,X:S),Z:S) f_2(ttrue,N:S,M:S,Y:S,X:S,Z:S) -> pair(X:S,add(M:S,Z:S)) f_3(pair(Y:S,Z:S),N:S,X:S) -> append(qsort(Y:S),add(X:S,qsort(Z:S))) lt(0,s(X:S)) -> ttrue lt(s(X:S),0) -> ffalse lt(s(X:S),s(Y:S)) -> lt(X:S,Y:S) qsort(add(N:S,X:S)) -> f_3(split(N:S,X:S),N:S,X:S) qsort(nil) -> nil split(N:S,add(M:S,Y:S)) -> f_1(split(N:S,Y:S),N:S,M:S,Y:S) split(N:S,nil) -> pair(nil,nil) -> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination. Problem 1: Dependency Pairs Processor: -> Pairs: APPEND(add(N:S,X:S),Y:S) -> APPEND(X:S,Y:S) F_1(pair(X:S,Z:S),N:S,M:S,Y:S) -> F_2(lt(N:S,M:S),N:S,M:S,Y:S,X:S,Z:S) F_1(pair(X:S,Z:S),N:S,M:S,Y:S) -> LT(N:S,M:S) F_3(pair(Y:S,Z:S),N:S,X:S) -> APPEND(qsort(Y:S),add(X:S,qsort(Z:S))) F_3(pair(Y:S,Z:S),N:S,X:S) -> QSORT(Y:S) F_3(pair(Y:S,Z:S),N:S,X:S) -> QSORT(Z:S) LT(s(X:S),s(Y:S)) -> LT(X:S,Y:S) QSORT(add(N:S,X:S)) -> F_3(split(N:S,X:S),N:S,X:S) QSORT(add(N:S,X:S)) -> SPLIT(N:S,X:S) SPLIT(N:S,add(M:S,Y:S)) -> F_1(split(N:S,Y:S),N:S,M:S,Y:S) SPLIT(N:S,add(M:S,Y:S)) -> SPLIT(N:S,Y:S) -> Rules: append(add(N:S,X:S),Y:S) -> add(N:S,append(X:S,Y:S)) append(nil,Y:S) -> Y:S f_1(pair(X:S,Z:S),N:S,M:S,Y:S) -> f_2(lt(N:S,M:S),N:S,M:S,Y:S,X:S,Z:S) f_2(ffalse,N:S,M:S,Y:S,X:S,Z:S) -> pair(add(M:S,X:S),Z:S) f_2(ttrue,N:S,M:S,Y:S,X:S,Z:S) -> pair(X:S,add(M:S,Z:S)) f_3(pair(Y:S,Z:S),N:S,X:S) -> append(qsort(Y:S),add(X:S,qsort(Z:S))) lt(0,s(X:S)) -> ttrue lt(s(X:S),0) -> ffalse lt(s(X:S),s(Y:S)) -> lt(X:S,Y:S) qsort(add(N:S,X:S)) -> f_3(split(N:S,X:S),N:S,X:S) qsort(nil) -> nil split(N:S,add(M:S,Y:S)) -> f_1(split(N:S,Y:S),N:S,M:S,Y:S) split(N:S,nil) -> pair(nil,nil) Problem 1: SCC Processor: -> Pairs: APPEND(add(N:S,X:S),Y:S) -> APPEND(X:S,Y:S) F_1(pair(X:S,Z:S),N:S,M:S,Y:S) -> F_2(lt(N:S,M:S),N:S,M:S,Y:S,X:S,Z:S) F_1(pair(X:S,Z:S),N:S,M:S,Y:S) -> LT(N:S,M:S) F_3(pair(Y:S,Z:S),N:S,X:S) -> APPEND(qsort(Y:S),add(X:S,qsort(Z:S))) F_3(pair(Y:S,Z:S),N:S,X:S) -> QSORT(Y:S) F_3(pair(Y:S,Z:S),N:S,X:S) -> QSORT(Z:S) LT(s(X:S),s(Y:S)) -> LT(X:S,Y:S) QSORT(add(N:S,X:S)) -> F_3(split(N:S,X:S),N:S,X:S) QSORT(add(N:S,X:S)) -> SPLIT(N:S,X:S) SPLIT(N:S,add(M:S,Y:S)) -> F_1(split(N:S,Y:S),N:S,M:S,Y:S) SPLIT(N:S,add(M:S,Y:S)) -> SPLIT(N:S,Y:S) -> Rules: append(add(N:S,X:S),Y:S) -> add(N:S,append(X:S,Y:S)) append(nil,Y:S) -> Y:S f_1(pair(X:S,Z:S),N:S,M:S,Y:S) -> f_2(lt(N:S,M:S),N:S,M:S,Y:S,X:S,Z:S) f_2(ffalse,N:S,M:S,Y:S,X:S,Z:S) -> pair(add(M:S,X:S),Z:S) f_2(ttrue,N:S,M:S,Y:S,X:S,Z:S) -> pair(X:S,add(M:S,Z:S)) f_3(pair(Y:S,Z:S),N:S,X:S) -> append(qsort(Y:S),add(X:S,qsort(Z:S))) lt(0,s(X:S)) -> ttrue
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