0.00/0.20 MAYBE 0.00/0.20 Input TRS: 0.00/0.20 AC symbols: plus times 0.00/0.20 1: 0(S()) -> S() 0.00/0.20 2: plus(S(),x) -> x 0.00/0.20 3: plus(0(x),0(y)) -> 0(plus(x,y)) 0.00/0.20 4: plus(0(x),1(y)) -> 1(plus(x,y)) 0.00/0.20 5: plus(0(x),j(y)) -> j(plus(x,y)) 0.00/0.20 6: plus(1(x),1(y)) -> j(plus(1(S()),plus(x,y))) 0.00/0.20 7: plus(j(x),j(y)) -> 1(plus(j(S()),plus(x,y))) 0.00/0.20 8: plus(1(x),j(y)) -> 0(plus(x,y)) 0.00/0.20 9: opp(S()) -> S() 0.00/0.20 10: opp(0(x)) -> 0(opp(x)) 0.00/0.20 11: opp(1(x)) -> j(opp(x)) 0.00/0.20 12: opp(j(x)) -> 1(opp(x)) 0.00/0.20 13: minus(x,y) -> plus(opp(y),x) 0.00/0.20 14: times(S(),x) -> S() 0.00/0.20 15: times(0(x),y) -> 0(times(x,y)) 0.00/0.20 16: times(1(x),y) -> plus(0(times(x,y)),y) 0.00/0.20 17: times(j(x),y) -> minus(0(times(x,y)),y) 0.00/0.20 18: sign(x) -> if_sign(x,S()) 0.00/0.20 19: if_sign(S(),x) -> x 0.00/0.20 20: if_sign(0(x),y) -> if_sign(x,y) 0.00/0.20 21: if_sign(1(x),y) -> if_sign(x,1(S())) 0.00/0.20 22: if_sign(j(x),y) -> if_sign(x,j(S())) 0.00/0.20 23: abs(x) -> if_abs(x,x,S()) 0.00/0.20 24: if_abs(0(x),y,z) -> if_abs(x,y,z) 0.00/0.20 25: if_abs(1(x),y,z) -> if_abs(x,y,1(S())) 0.00/0.20 26: if_abs(j(x),y,z) -> if_abs(x,y,j(S())) 0.00/0.20 27: if_abs(S(),x,S()) -> S() 0.00/0.20 28: if_abs(S(),x,1(S())) -> x 0.00/0.20 29: if_abs(S(),x,j(S())) -> opp(x) 0.00/0.20 30: min(x,y) -> if_min(minus(abs(y),abs(x)),x,y,S()) 0.00/0.20 31: min'(x,y) -> if_min(minus(abs(1(y)),abs(1(x))),x,y,S()) 0.00/0.20 32: min''(x,y) -> if_min(minus(abs(j(y)),abs(j(x))),x,y,S()) 0.00/0.20 33: if_min(0(x),y,z,u) -> if_min(x,y,z,u) 0.00/0.20 34: if_min(1(x),y,z,u) -> if_min(x,y,z,1(S())) 0.00/0.20 35: if_min(j(x),y,z,u) -> if_min(x,y,z,j(S())) 0.00/0.20 36: if_min(S(),x,y,S()) -> x 0.00/0.20 37: if_min(S(),x,y,1(S())) -> x 0.00/0.20 38: if_min(S(),x,y,j(S())) -> y 0.00/0.20 Number of strict rules: 38 0.00/0.20 Direct POLO(bPol) ... failed. 0.00/0.20 Uncurrying ... failed. 0.00/0.20 Dependency Pairs: 0.00/0.20 #1: #if_abs(S(),x,j(S())) -> #opp(x) 0.00/0.20 #2: #if_min(j(x),y,z,u) -> #if_min(x,y,z,j(S())) 0.00/0.20 #3: #plus(1(x),1(y)) -> #plus(1(S()),plus(x,y)) 0.00/0.20 #4: #plus(1(x),1(y)) -> #plus(x,y) 0.00/0.20 #5: #times(x,times(y,z)) ->= #times(times(x,y),z) 0.00/0.20 #6: #times(x,times(y,z)) ->= #times(x,y) 0.00/0.20 #7: #minus(x,y) -> #plus(opp(y),x) 0.00/0.20 #8: #minus(x,y) -> #opp(y) 0.00/0.20 #9: #opp(1(x)) -> #opp(x) 0.00/0.20 #10: #if_abs(0(x),y,z) -> #if_abs(x,y,z) 0.00/0.20 #11: #abs(x) -> #if_abs(x,x,S()) 0.00/0.20 #12: #opp(j(x)) -> #opp(x) 0.00/0.20 #13: #min'(x,y) -> #if_min(minus(abs(1(y)),abs(1(x))),x,y,S()) 0.00/0.20 #14: #min'(x,y) -> #minus(abs(1(y)),abs(1(x))) 0.00/0.20 #15: #min'(x,y) -> #abs(1(y)) 0.00/0.20 #16: #min'(x,y) -> #abs(1(x)) 0.00/0.20 #17: #min(x,y) -> #if_min(minus(abs(y),abs(x)),x,y,S()) 0.00/0.20 #18: #min(x,y) -> #minus(abs(y),abs(x)) 0.00/0.20 #19: #min(x,y) -> #abs(y) 0.00/0.20 #20: #min(x,y) -> #abs(x) 0.00/0.20 #21: #if_abs(1(x),y,z) -> #if_abs(x,y,1(S())) 0.00/0.20 #22: #if_sign(0(x),y) -> #if_sign(x,y) 0.00/0.20 #23: #plus(j(x),j(y)) -> #plus(j(S()),plus(x,y)) 0.00/0.20 #24: #plus(j(x),j(y)) -> #plus(x,y) 0.00/0.20 #25: #plus(x,plus(y,z)) ->= #plus(plus(x,y),z) 0.00/0.20 #26: #plus(x,plus(y,z)) ->= #plus(x,y) 0.00/0.20 #27: #opp(0(x)) -> #0(opp(x)) 0.00/0.20 #28: #opp(0(x)) -> #opp(x) 0.00/0.20 #29: #if_min(0(x),y,z,u) -> #if_min(x,y,z,u) 0.00/0.20 #30: #plus(0(x),j(y)) -> #plus(x,y) 0.00/0.20 #31: #if_sign(j(x),y) -> #if_sign(x,j(S())) 0.00/0.20 #32: #if_min(1(x),y,z,u) -> #if_min(x,y,z,1(S())) 0.00/0.20 #33: #times(j(x),y) -> #minus(0(times(x,y)),y) 0.00/0.20 #34: #times(j(x),y) -> #0(times(x,y)) 0.00/0.20 #35: #times(j(x),y) -> #times(x,y) 0.00/0.20 #36: #min''(x,y) -> #if_min(minus(abs(j(y)),abs(j(x))),x,y,S()) 0.00/0.20 #37: #min''(x,y) -> #minus(abs(j(y)),abs(j(x))) 0.00/0.20 #38: #min''(x,y) -> #abs(j(y)) 0.00/0.20 #39: #min''(x,y) -> #abs(j(x)) 0.00/0.20 #40: #if_abs(j(x),y,z) -> #if_abs(x,y,j(S())) 0.00/0.20 #41: #if_sign(1(x),y) -> #if_sign(x,1(S())) 0.00/0.20 #42: #times(1(x),y) -> #plus(0(times(x,y)),y) 0.00/0.20 #43: #times(1(x),y) -> #0(times(x,y)) 0.00/0.20 #44: #times(1(x),y) -> #times(x,y) 0.00/0.20 #45: #plus(0(x),0(y)) -> #0(plus(x,y)) 0.00/0.20 #46: #plus(0(x),0(y)) -> #plus(x,y) 0.00/0.20 #47: #plus(1(x),j(y)) -> #0(plus(x,y)) 0.00/0.20 #48: #plus(1(x),j(y)) -> #plus(x,y) 0.00/0.20 #49: #times(0(x),y) -> #0(times(x,y)) 0.00/0.20 #50: #times(0(x),y) -> #times(x,y) 0.00/0.20 #51: #plus(0(x),1(y)) -> #plus(x,y) 0.00/0.20 #52: #sign(x) -> #if_sign(x,S()) 0.00/0.20 Number of SCCs: 6, DPs: 27 0.00/0.20 SCC { #9 #12 #28 } 0.00/0.20 POLO(Sum)... succeeded. 0.00/0.20 #0 w: 0 0.00/0.20 min' w: 0 0.00/0.20 1 w: x1 + 1 0.00/0.20 #if_abs w: 0 0.00/0.20 S w: 0 0.00/0.20 minus w: 0 0.00/0.20 #if_min w: 0 0.00/0.20 #plus w: 0 0.00/0.20 if_abs w: 0 0.00/0.20 #min w: 0 0.00/0.20 #min' w: 0 0.00/0.20 #abs w: 0 0.00/0.20 min'' w: 0 0.00/0.20 abs w: 0 0.00/0.20 #opp w: x1 0.00/0.20 #min'' w: 0 0.00/0.20 sign w: 0 0.00/0.20 #times w: 0 0.00/0.20 0 w: x1 + 1 0.00/0.20 times w: 0 0.00/0.20 j w: x1 + 1 0.00/0.20 if_sign w: 0 0.00/0.20 #minus w: 0 0.00/0.20 opp w: 0 0.00/0.20 plus w: 0 0.00/0.20 min w: 0 0.00/0.20 #if_sign w: 0 0.00/0.20 if_min w: 0 0.00/0.20 #sign w: 0 0.00/0.20 USABLE RULES: { } 0.00/0.20 Removed DPs: #9 #12 #28 0.00/0.20 Number of SCCs: 5, DPs: 24 0.00/0.20 SCC { #22 #31 #41 } 0.00/0.20 POLO(Sum)... succeeded. 0.00/0.20 #0 w: 0 0.00/0.20 min' w: 0 0.00/0.20 1 w: x1 + 1 0.00/0.20 #if_abs w: 0 0.00/0.20 S w: 1 0.00/0.20 minus w: 0 0.00/0.20 #if_min w: 0 0.00/0.20 #plus w: 0 0.00/0.20 if_abs w: 0 0.00/0.20 #min w: 0 0.00/0.20 #min' w: 0 0.00/0.20 #abs w: 0 0.00/0.20 min'' w: 0 0.00/0.20 abs w: 0 0.00/0.20 #opp w: 0 0.00/0.20 #min'' w: 0 0.00/0.20 sign w: 0 0.00/0.20 #times w: 0 0.00/0.20 0 w: x1 + 1 0.00/0.20 times w: 0 0.00/0.20 j w: x1 + 1 0.00/0.20 if_sign w: 0 0.00/0.20 #minus w: 0 0.00/0.20 opp w: 0 0.00/0.20 plus w: 0 0.00/0.20 min w: 0 0.00/0.20 #if_sign w: x1 0.00/0.20 if_min w: 0 0.00/0.20 #sign w: 0 0.00/0.20 USABLE RULES: { } 0.00/0.20 Removed DPs: #22 #31 #41 0.00/0.20 Number of SCCs: 4, DPs: 21 0.00/0.20 SCC { #10 #21 #40 } 0.00/0.20 POLO(Sum)... succeeded. 0.00/0.20 #0 w: 0 0.00/0.20 min' w: 0 0.00/0.20 1 w: x1 + 1 0.00/0.20 #if_abs w: x1 0.00/0.20 S w: 1 0.00/0.20 minus w: 0 0.00/0.20 #if_min w: 0 0.00/0.20 #plus w: 0 0.00/0.20 if_abs w: 0 0.00/0.20 #min w: 0 0.00/0.20 #min' w: 0 0.00/0.20 #abs w: 0 0.00/0.20 min'' w: 0 0.00/0.20 abs w: 0 0.00/0.20 #opp w: 0 0.00/0.20 #min'' w: 0 0.00/0.20 sign w: 0 0.00/0.20 #times w: 0 0.00/0.20 0 w: x1 + 1 0.00/0.20 times w: 0 0.00/0.20 j w: x1 + 1 0.00/0.20 if_sign w: 0 0.00/0.20 #minus w: 0 0.00/0.20 opp w: 0 0.00/0.20 plus w: 0 0.00/0.20 min w: 0 0.00/0.20 #if_sign w: 0 0.00/0.20 if_min w: 0 0.00/0.20 #sign w: 0 0.00/0.20 USABLE RULES: { } 0.00/0.20 Removed DPs: #10 #21 #40 0.00/0.20 Number of SCCs: 3, DPs: 18 0.00/0.20 SCC { #2 #29 #32 } 0.00/0.20 POLO(Sum)... succeeded. 0.00/0.20 #0 w: 0 0.00/0.20 min' w: 0 0.00/0.20 1 w: x1 + 1 0.00/0.20 #if_abs w: 0 0.00/0.20 S w: 1 0.00/0.20 minus w: 0 0.00/0.20 #if_min w: x1 0.00/0.20 #plus w: 0 0.00/0.20 if_abs w: 0 0.00/0.20 #min w: 0 0.00/0.20 #min' w: 0 0.00/0.20 #abs w: 0 0.00/0.20 min'' w: 0 0.00/0.20 abs w: 0 0.00/0.20 #opp w: 0 0.00/0.20 #min'' w: 0 0.00/0.20 sign w: 0 0.00/0.20 #times w: 0 0.00/0.20 0 w: x1 + 1 0.00/0.20 times w: 0 0.00/0.20 j w: x1 + 1 0.00/0.20 if_sign w: 0 0.00/0.20 #minus w: 0 0.00/0.20 opp w: 0 0.00/0.20 plus w: 0 0.00/0.20 min w: 0 0.00/0.20 #if_sign w: 0 0.00/0.20 if_min w: 0 0.00/0.20 #sign w: 0 0.00/0.20 USABLE RULES: { } 0.00/0.20 Removed DPs: #2 #29 #32 0.00/0.20 Number of SCCs: 2, DPs: 15 0.00/0.20 SCC { #5 #6 #35 #44 #50 } 0.00/0.20 POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... succeeded. 0.00/0.20 #0 w: max(x1 - 1, 0) 0.00/0.20 min' w: max(x1 - 1, 0) 0.00/0.20 1 w: max(x1, 0) 0.00/0.20 #if_abs w: 0 0.00/0.20 S w: 0 0.00/0.20 minus w: max(x1, x2 + 2, 0) 0.00/0.20 #if_min w: 0 0.00/0.20 #plus w: 0 0.00/0.20 if_abs w: max(x2 - 1, 0) 0.00/0.20 #min w: max(x1 - 1, 0) 0.00/0.20 #min' w: 0 0.00/0.20 #abs w: max(x1 - 1, 0) 0.00/0.20 min'' w: 0 0.00/0.20 abs w: 0 0.00/0.20 #opp w: max(x1 - 1, 0) 0.00/0.20 #min'' w: 0 0.00/0.20 sign w: 0 0.00/0.20 #times w: max(x1 + x2 - 1, 0) 0.00/0.20 0 w: max(x1, 0) 0.00/0.20 times w: max(x1 + x2 + 2, 0) 0.00/0.20 j w: max(x1, 0) 0.00/0.20 if_sign w: max(x2 - 1, 0) 0.00/0.20 #minus w: 0 0.00/0.20 opp w: 0 0.00/0.20 plus w: max(x1, x2, 0) 0.00/0.20 min w: max(x1 - 1, 0) 0.00/0.20 #if_sign w: max(x1 - 1, 0) 0.00/0.20 if_min w: 0 0.00/0.20 #sign w: 0 0.00/0.20 USABLE RULES: { 1..17 39 40 } 0.00/0.20 Removed DPs: #6 0.00/0.20 Number of SCCs: 2, DPs: 14 0.00/0.20 SCC { #5 #35 #44 #50 } 0.00/0.20 POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... Mat2b... failed. 0.00/0.20 Finding a loop... failed. 0.00/0.20 EOF