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TRS Standard pair #487071486
details
property
value
status
complete
benchmark
PEANO_complete_Z.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n179.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
NaTT v.1.6c
configuration
Default
runtime (wallclock)
0.110521 seconds
cpu usage
0.038938
user time
0.02113
system time
0.017808
max virtual memory
113188.0
max residence set size
9244.0
stage attributes
key
value
starexec-result
YES
output
YES Input TRS: 1: U11(tt(),V1,V2) -> U12(isNat(activate(V1)),activate(V2)) 2: U12(tt(),V2) -> U13(isNat(activate(V2))) 3: U13(tt()) -> tt() 4: U21(tt(),V1) -> U22(isNat(activate(V1))) 5: U22(tt()) -> tt() 6: U31(tt(),N) -> activate(N) 7: U41(tt(),M,N) -> s(plus(activate(N),activate(M))) 8: and(tt(),X) -> activate(X) 9: isNat(n__0()) -> tt() 10: isNat(n__plus(V1,V2)) -> U11(and(isNatKind(activate(V1)),n__isNatKind(activate(V2))),activate(V1),activate(V2)) 11: isNat(n__s(V1)) -> U21(isNatKind(activate(V1)),activate(V1)) 12: isNatKind(n__0()) -> tt() 13: isNatKind(n__plus(V1,V2)) -> and(isNatKind(activate(V1)),n__isNatKind(activate(V2))) 14: isNatKind(n__s(V1)) -> isNatKind(activate(V1)) 15: plus(N,0()) -> U31(and(isNat(N),n__isNatKind(N)),N) 16: plus(N,s(M)) -> U41(and(and(isNat(M),n__isNatKind(M)),n__and(isNat(N),n__isNatKind(N))),M,N) 17: 0() -> n__0() 18: plus(X1,X2) -> n__plus(X1,X2) 19: isNatKind(X) -> n__isNatKind(X) 20: s(X) -> n__s(X) 21: and(X1,X2) -> n__and(X1,X2) 22: activate(n__0()) -> 0() 23: activate(n__plus(X1,X2)) -> plus(X1,X2) 24: activate(n__isNatKind(X)) -> isNatKind(X) 25: activate(n__s(X)) -> s(X) 26: activate(n__and(X1,X2)) -> and(X1,X2) 27: activate(X) -> X Number of strict rules: 27 Direct POLO(bPol) ... failed. Uncurrying ... failed. Dependency Pairs: #1: #U12(tt(),V2) -> #U13(isNat(activate(V2))) #2: #U12(tt(),V2) -> #isNat(activate(V2)) #3: #U12(tt(),V2) -> #activate(V2) #4: #U31(tt(),N) -> #activate(N) #5: #isNatKind(n__plus(V1,V2)) -> #and(isNatKind(activate(V1)),n__isNatKind(activate(V2))) #6: #isNatKind(n__plus(V1,V2)) -> #isNatKind(activate(V1)) #7: #isNatKind(n__plus(V1,V2)) -> #activate(V1) #8: #isNatKind(n__plus(V1,V2)) -> #activate(V2) #9: #isNat(n__s(V1)) -> #U21(isNatKind(activate(V1)),activate(V1)) #10: #isNat(n__s(V1)) -> #isNatKind(activate(V1)) #11: #isNat(n__s(V1)) -> #activate(V1) #12: #isNat(n__s(V1)) -> #activate(V1) #13: #activate(n__isNatKind(X)) -> #isNatKind(X) #14: #activate(n__plus(X1,X2)) -> #plus(X1,X2) #15: #isNatKind(n__s(V1)) -> #isNatKind(activate(V1)) #16: #isNatKind(n__s(V1)) -> #activate(V1) #17: #activate(n__s(X)) -> #s(X) #18: #U41(tt(),M,N) -> #s(plus(activate(N),activate(M))) #19: #U41(tt(),M,N) -> #plus(activate(N),activate(M)) #20: #U41(tt(),M,N) -> #activate(N) #21: #U41(tt(),M,N) -> #activate(M) #22: #isNat(n__plus(V1,V2)) -> #U11(and(isNatKind(activate(V1)),n__isNatKind(activate(V2))),activate(V1),activate(V2)) #23: #isNat(n__plus(V1,V2)) -> #and(isNatKind(activate(V1)),n__isNatKind(activate(V2))) #24: #isNat(n__plus(V1,V2)) -> #isNatKind(activate(V1)) #25: #isNat(n__plus(V1,V2)) -> #activate(V1) #26: #isNat(n__plus(V1,V2)) -> #activate(V2) #27: #isNat(n__plus(V1,V2)) -> #activate(V1) #28: #isNat(n__plus(V1,V2)) -> #activate(V2) #29: #activate(n__0()) -> #0() #30: #activate(n__and(X1,X2)) -> #and(X1,X2) #31: #plus(N,s(M)) -> #U41(and(and(isNat(M),n__isNatKind(M)),n__and(isNat(N),n__isNatKind(N))),M,N) #32: #plus(N,s(M)) -> #and(and(isNat(M),n__isNatKind(M)),n__and(isNat(N),n__isNatKind(N))) #33: #plus(N,s(M)) -> #and(isNat(M),n__isNatKind(M)) #34: #plus(N,s(M)) -> #isNat(M) #35: #plus(N,s(M)) -> #isNat(N) #36: #U11(tt(),V1,V2) -> #U12(isNat(activate(V1)),activate(V2)) #37: #U11(tt(),V1,V2) -> #isNat(activate(V1)) #38: #U11(tt(),V1,V2) -> #activate(V1) #39: #U11(tt(),V1,V2) -> #activate(V2) #40: #and(tt(),X) -> #activate(X) #41: #plus(N,0()) -> #U31(and(isNat(N),n__isNatKind(N)),N) #42: #plus(N,0()) -> #and(isNat(N),n__isNatKind(N)) #43: #plus(N,0()) -> #isNat(N) #44: #U21(tt(),V1) -> #U22(isNat(activate(V1))) #45: #U21(tt(),V1) -> #isNat(activate(V1)) #46: #U21(tt(),V1) -> #activate(V1) Number of SCCs: 1, DPs: 41 SCC { #2..16 #19..28 #30..43 #45 #46 } POLO(Sum)... succeeded. #0 w: 0 isNatKind w: x1 + 31599 U21 w: x1 + x2 + 9 U11 w: x1 + x2 + 3 s w: x1 + 2 #isNat w: x1 + 1 activate w: x1 n__isNatKind w: x1 + 31599 and w: x2 + 2 #plus w: x1 + x2 + 31602 #activate w: x1 + 1 #U13 w: 0 U12 w: x2 + 12 n__s w: x1 + 2 #U12 w: x2 + 2 0 w: 3 #s w: 0 n__plus w: x1 + x2 + 31602
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